Computer Networks 55 (2011) 856–872
Contents lists available at ScienceDirect
Computer Networks
journal homepage: www.elsevier.com/locate/comnet
Energy-efficient geographic routing in the presence of localization errors
B. Peng ⇑, A.H. Kemp
School of Electronic and Electrical Engineering, University of Leeds, Leeds, United Kingdom
a r t i c l e
i n f o
Article history:
Received 8 February 2010
Received in revised form 16 October 2010
Accepted 31 October 2010
Available online 10 November 2010
Responsible Editor: W. Lou
Keywords:
Wireless Sensor Networks
Energy efficiency
Geographic routing
Location errors
a b s t r a c t
Existing energy-efficient geographic routing algorithms have been shown to reduce energy
consumption and hence prolong the lifetime of multi-hop wireless networks. However, in
practical deployment scenarios, where location errors inevitably exist, these algorithms are
vulnerable to a substantial performance degradation not only in terms of packet delivery
ratio but also energy consumption. This paper focuses on the fundamental impact of localization errors in the design of energy-efficient geographic routing algorithms. First, we analyze the properties of existing energy-efficient geographic routing algorithms. This is then
extended to compare these energy-efficient geographical routing algorithms in the presence of localization errors. The main contribution of this section is an in-depth analysis
of the impact of location errors on geographic routing in terms of energy efficiency. By
incorporating location error statistics into an objective function, we propose a new
energy-efficient geographic routing algorithm named LED. An adaptive transmission strategy is then proposed to cope with the transmission failure caused by location errors.
Finally, extensive performance evaluations show that our proposal is robust to location
errors, thus statistically minimizing consumed transmit power as a packet is relayed from
source to destination.
Ó 2010 Elsevier B.V. All rights reserved.
1. Introduction
Wireless Sensor Networks (WSNs) will be deployed on a
large scale in the near future for numerous applications. In
these applications, the wireless nodes are typically battery
operated. Therefore they need to conserve power to maximize node life and thus of the network itself. Since routing
is an essential function in these networks, developing an
energy (power)-aware routing protocol in WSNs is a
challenging area and has attracted much research effort
in recent years [1,2]. One crucial problem is to find a power
efficient route between source and destination nodes.
Moreover, if nodes can adjust their transmission power,
then the power metric will depend on the distance
between nodes.
Among different energy efficient routing techniques,
geographic routing (aka location or position-based routing)
⇑ Corresponding author.
E-mail address: peng_bo@hotmail.com (B. Peng).
1389-1286/$ - see front matter Ó 2010 Elsevier B.V. All rights reserved.
doi:10.1016/j.comnet.2010.10.020
has been deemed to be the most promising solution for
critically energy-constrained multi-hop wireless networks
(see [1–5]). It assumes that all nodes in a network have the
knowledge of their own location either via GPS receivers
attached to them or through network localization algorithms1 [6]. When a node has packets to send, it will select
a next forwarding node only based on the location of itself,
its neighbours and the ultimate destination. The locations
of the neighbours are typically learned via one-hop broadcast, while the location of the destination is obtained using
a so called location service [4]. Hence all operations are
strictly local, that is, every node is required to keep track
only of its direct neighbours. Therefore, geographic routing
can scale well to a large number of network nodes having
no requirement of the establishment or maintenance of a
route. These two factors, i.e. absence of the necessity to keep
routing tables up to date and independence of remotely
1
The cost to obtain location information can be quite large and is a topic
of research in its own right.
B. Peng, A.H. Kemp / Computer Networks 55 (2011) 856–872
occurring topology changes, are among the foremost reasons
why geographic routing is exceptionally suitable for operation in sensor networks [7]. However, since location is the
only information required for geographical routing to deliver
packets from the source to the destination node, the availability and accuracy of the available locations is crucial.
Previous work in [8–11] has shown that location errors
can lead to a substantial degradation in the performance of
geographic routing in terms of packet delivery ratio (PDR).
Several schemes and fixes have been proposed to mitigate
the impact on routing performance. However, the impact
of location error has been evaluated only in terms of packet
delivery ratio, the impact of location errors on the power
consumption of geographic routing algorithms has not
been investigated.
In this paper, a detailed study of the impact of location
errors on energy efficient geographic routing algorithms is
provided. The results of the analysis show a clear need of
an energy efficient geographic routing protocol which can
also tolerate location errors. To achieve this purpose, a novel, robust, energy aware geographic routing scheme is
proposed. By incorporating location error statistics into a
routing objective function, the proposal is shown to be
robust in the inevitable presence of location errors. Thus
it statistically minimizes consumed transmit power as a
packet is relayed from source node to destination node.
The main contributions of this paper are the following.
Proof that the two approaches of existing energy-efficient geographic routing algorithms lead to an identical
optimal position for each hop.
A detailed study of the impact of location error on existing geographic routing algorithms.
Proposal of a novel, energy-efficient geographic forwarding scheme which can statistically minimize total
path energy consumption in the presence of location
errors.
Introduction of an adaptive transmission range control
strategy to improve the PDR for power (and hence
transmission range) adjustable routing algorithms.
The paper is organized as follows. Section 2 provides a
review of existing routing algorithms to cope with location
errors and energy consumption. Then two different
approaches of existing power-saving routing algorithms
are analyzed in Section 3. A detailed study of the effect of
the location errors on power-efficient geographic routing
is provided in Section 4. Based on the observation from
previous sections, a new robust power-saving routing algorithm and an adaptive transmission strategy are proposed
in Section 5. The performance evaluation of our proposal is
given in Section 6. Finally, Section 7 concludes the paper.
2. Background and related work
Geographic routing has been widely recognized as a
class of routing protocol in mobile ad hoc and sensor networks. One of the biggest advantages of geographic routing
is the small overhead due to its local operation, which
eliminates the route setup and setup time. So, this
857
combination of these features makes geographical routing
especially attractive for WSNs. The vast majority of the discussions about geographical routing so far assume the
location of each node is known perfectly accurately. However, in reality, localization techniques can only provide
location with limited accuracy, and their accuracy has
shown to be variable due to operating environment.
In the area of localization, location error is defined as
the distance between real location and the estimated location. It is normalized as the percentage of the transmission
range of a localization system. The error may lead to incorrect operation in the geographic routing process. The reasons can be either inaccurate ranging measurements or
algorithmic artifacts. Localization in WSNs varies from traditional global positioning system (GPS) and cellular networks localization techniques in that sensor nodes are
assumed to be small in size, simple, of low power consumption and cooperatively deployed in large numbers.
Numerous localization algorithms for WSNs have been
proposed and are mainly categorized as distance-based
or connectivity-based.
Distance-based algorithms use inter-node distance
measurement to locate the unknown nodes in the network.
This type of localization algorithm generally provides better accuracy than the connectivity-based algorithms. The
work in [12] divided the whole sensor network field into
small groups where adjacent groups may share common
sensors. Multidimensional scaling (MDS) is used to estimate the location of sensors in each group. In the simulation evaluation, the distance error was assumed to be
uniformly distributed in the range of 0–50% of the transmission range. As a result, the final location estimation is
in the range of 10–45% of the transmission range. The
scheme proposed in [13] is similar to the ‘‘DV-hop’’ algorithm to obtain an initial estimate of the node location.
Then, the measured distances between neighbour nodes
are used to refine the location estimation iteratively. The
simulation results showed that this algorithm can achieve
a mean localization error of less than 33% of the transmission range when the distance measurement error is 5% of
the transmission range.
The work in [14] proposed a connectivity metric to
measure the quality of the wireless link between a pair
of neighbours. Empirical results showed that the localization error falls within 30% of the separations distance
between two adjacent reference points [6]. The ‘‘DV-hop’’
approach proposed in [15] use hop-count to estimate the
distance between anchor nodes and unknown nodes. This
algorithm was simulated with a total of 100 nodes uniformly distributed in across circle. Simulation showed that
this algorithm has a mean error of 45% transmission range
with 10% anchors. When the number of anchors is
increased to 20%, the mean localization error reduced to
30% of the transmission range. The work in [16] formulated
the connectivity-based localization as a convex optimization problem. The algorithm was simulated with 200 nodes
in a square of 10R 10R, where R is the transmission
range. Simulation showed that the mean localization error
is a monotonically decreasing function of the number of
anchor nodes. The mean localization error is as high as
the transmission range when the number of anchor nodes
858
B. Peng, A.H. Kemp / Computer Networks 55 (2011) 856–872
is 18. It reduced to 50% of the transmission range when the
number of anchors increase to 50.
Compared with distance-based localization algorithms,
the most attractive feature of connectivity-based localization algorithms is their simplicity. No additional hardware
is required to perform the localization. However, as discussed above, the accuracy they can offer is limited. Localization error from a connectivity-based algorithm is also
driven by a number of network settings, such as the density, number of anchors and topology.
Previous studies [8,10,17,18] have shown that Localization errors can lead to substantial degradation in the
performance of geographic routing in terms of packet delivery ratio and energy consumption. As discussed above,
some systems are more accurate (e.g. distance-based localization algorithms) than others (e.g. connectivity-based
localization algorithms), however, it would be prudent to
ensure that geographic routing are robust to location errors
that are at the higher end of the expected error.
The study in [17] found that the packet delivery rate
and path length remain acceptable up to location error of
40% of the transmission range. However, no theoretical error model was given and the conclusion was based on the
simulation results. The impact of location inaccuracy and
inconsistency on both greedy forwarding and recovery
procedure has been studied separately in [8]. By modelling
four location inaccuracy metrics: absolute location accuracy, relative distance accuracy, absolute location inconsistency and relative distance inconsistency, they observed
severe performance degradation and protocol correctness
violations for greedy forwarding even in the presence of
reasonable (relatively small) location errors.
The effect of localization errors on recovery procedures
have also been studied in [9], where the authors focused on
the perimeter forwarding (also known as face routing) in
Greedy Perimeter Stateless Routing (GPSR). Their results
showed that even for realistic and relatively small location
errors (10%), the effects of location errors on perimeter forwarding are noticeable. The direct impact of several localization characteristics of sensor networks on geographic
routing has been firstly studied in [11], and the results
showed that the number of anchor nodes, the noise level,
the radio range and the respective number of connections
each have a significant impact on GPSR routing performance, which gave insights into the source of location
errors.
The only study that addressed the impact of location error on the power consumption of geographic routing is
found in [18]. It showed that the throughput and energy
consumption performance in the network deteriorates
considerably for localization errors of more than 20% of
the radio range. By using the second order neighbourhood
information, a new routing scheme was proposed to reduce the performance deterioration with location errors
on both packet delivery rate and energy consumption. This
work also took the obstacles into the consideration when
studying the effect of localization error, which provided a
useful guide for the localization accuracies and node densities needed to achieve reasonable routing performance.
However, Shah et al. [18] only studied basic geographic
routing which uses greedy forwarding to send the packet
to the neighbours closest to the destination. Energy efficient geographic routing with variable transmission range
has not been addressed in this work. In addition, the location error in their study is uniformly distributed between
zero and the maximum error, which is not the preferred
model. Numerous previous work in the localization field
(e.g. [30–32]) has studied the sources of errors (such as
the accuracy of measurements, network density, uncertainties in anchor locations, etc.) which impact localization, and found that all these factors contribute to the
final error in a location estimate. Therefore, a Gaussian distribution is more appropriate to model location errors due
to the many uncertainties involved in localization. This
model has also been used in [10,19].
A more realistic scenario where nodes have imperfect
circular transmission patterns and the transmission ranges
deviate from the ideal disk model has been investigated in
[10]. The authors developed a theoretical error model
which follows a 2-D Gaussian distribution and proved that
greedy forwarding suffers both transmission failure and
backward progress. By incorporating location errors in
their algorithm, they showed that their Maximum Expectation within transmission Range (MER) algorithm is robust
to location errors. However, no energy constraint was considered in their study.
Different from the basics greedy forwarding, energy
efficient geographic routing algorithms try to deliver a
packet with minimum power consumption from source
to destination. By assuming an adjustable transmission
range, Stojmenovic and Lin [3] found that the maximal
power saving could be achieved by using additional intermediate nodes which might be available at a desired location. They further derived the optimal location (i.e. optimal
transmission range) for the next forwarding nodes and the
minimal end-to-end power consumption via these nodes.
This provided the basis for several power efficient geographic routing algorithms which attempt to minimize
the total power needed. The optimization of transmission
range as a system design issue was studied in [20]. Similar
conclusion has been drawn that the optimal transmission
range that minimizes the total energy consumption is
independent of the physical network topology, the number
of transmission sources, and the total end-to-end distance.
Only the propagation environment (and hence power decay profile exponent) and radio transceiver device parameters effect the optimal transmission range. Another study
in [21] investigated the selection of optimal transmission
power for ad hoc networks. Based on an analytical model
for network-wide energy consumption, parameterized by
density, packet size, MAC protocol and radio characteristics, they derived the same expression of optimal transmission function which only depended on the propagation loss
factor and device parameters.
In this paper, the impact of location error on the power
efficient geographical routing algorithm is investigated.
Assuming knowledge of the statistical error associated
with each node, a robust geographic routing algorithm is
designed which is not only power efficient, but also tolerant to the location errors inevitably existing in a network.
Simulation evaluations were performed to validate the
proposal. Unless otherwise stated, the term ‘‘location
B. Peng, A.H. Kemp / Computer Networks 55 (2011) 856–872
error’’ refers to ‘‘location error due to inaccurate measurement’’ throughout this paper. In a mobile environment,
location error could be caused by displacement due to
mobility. A number of methods have been proposed to
cope with this inaccuracy due to node mobility, e.g., see
[22], but we do not include it in this preliminary study.
In summary, compared with the studies in [8–11,17], this
study not only investigates the impact of location error
on PDR, but also on energy consumptions. Compared with
[18], this study investigates the energy-efficient geographic routing with adjustable radio transmission range
to maximize the energy efficiency, while Shah et al. [18]
only studied the basic greedy forwarding scheme with
flooding mechanism when packet get stuck due to a network void. Compared with [3,20,21], Gaussian distributed
location errors are introduced on node coordinates to
study the effect on energy-efficient geographic routing.
For the convenience of the reader, let us introduce the following definitions.
Definition 1. Given a source node S and a destination node
D, the progress of a generic node I is the distance between S
and D minus the distance between I and D.
Definition 2. A graph G is connected if, for every pair of
nodes i and j, there is a route from i to j.
3. Analysis of existing energy-efficient routing
algorithms
Prior to discussing the impact of localization errors, it is
necessary to understand the mechanism behind the design
of energy efficient geographic routing. Understanding the
design of energy efficient geographic routing not only provides a baseline of the performance of each existing routing algorithm in an error free environment, but also
establishes the theoretical foundation to develop a robust
energy efficient geographic routing algorithm in the presence of location errors. Therefore, in this section, the design of energy efficient geographic routing is discussed
by initially assuming no location errors are present. First,
we provide a theoretical proof that alternative existing
approaches to determine the optimal next forwarding
location, to achieve maximum energy saving, reach the
same outcome. Then, a number of existing energy efficient
geographic routing algorithms are compared in terms of
their energy consumption and hop count with three
different propagation loss exponents (to mimic different
propagation environments).
3.1. Energy model and optimum transmission range
In the power efficient routing field, there are two
approaches to calculate the optimal position to forward
packets in terms of end-to-end power consumption per
packet. Previous work in [3,20,21,23] all belong to the first
approach which uses total path energy consumption as the
metric. These approaches reach a similar conclusion that
there exists an optimal next forwarding position (or
characteristic distance as in [23]) for the total energy con-
859
sumption of a path to be minimized. Moreover, this position has been shown to only depend on the propagation
loss factor and device parameters. While, the second approach, as in [24,25], uses the one-hop metric named distance-energy efficiency which is defined as the ratio of
the progress of a packet during its one-hop transmission
and the energy consumption of that transmission. Then,
by choosing the next relay node along a path which maximizes the distance-energy efficiency of each hop, this approach will be able to save the energy of the path. They
also argued that this one-hop distance-energy efficiency
should be consistent with the overall distance-energy efficiency of the entire path in a homogeneous environment.
However, this argument was only validated through simulation in their work which showed the similar performance
of the power consumption of the two approaches. Another
work [26] uses the definition of power spent per unit of
progress made, which is the inverse of the distance-energy
efficiency. Therefore, the routing algorithm proposed in
[26] selects the neighbour which minimizes the power
spent per unit of progress made in each hop.
Here, we prove the optimal position these two approaches calculate to achieve best end-to-end power saving per packet is identical. First, a general model for
power consumption per bit at the physical layer is used
as in [27]. It assumes a simple model for the radio hardware energy dissipation where the transmitter dissipates
energy to run the radio electronics and the power amplifier, and the receiver dissipates energy to run the radio
electronics. Total energy e is given by:
e ¼ eTx þ eRx ¼ eTx-amp þ eTx-elec þ eRx-elec ;
ð1Þ
where eTx is the total energy consumed at the transmitter
to operate the radio electronics (eTx-elec) and power amplifier (eTx-amp). eRx-elec is the energy consumed for radio electronics at the receiver. The amplifier energy, eTx-amp, is
dependent on ensuring an acceptable SNR (and hence
acceptable power limited bit error rate) at distance d. It
is calculated as bda. Where a is the path loss index and b
is a constant [Joule/bit/ma]. The electronics energy, eelec
[Joule/bit], depends on the factors such as processing,
encoding, and decoding at each node. As in [27], we take
the simplifying assumption that:
eTx-elec ¼ eRx-elec ¼ eelec :
ð2Þ
Thus the overall expression for e in (1) simplifies to
e ¼ bda þ c;
ð3Þ
where c = 2 eelec.
Theorem. The optimal next node position calculated by the
end-to-end optimization of total energy consumption of a
path is identical to the position obtained through hop by hop
optimization of progress per unit of energy in total energy
consumption perspective, and the distance between the
position and the source (or intermediate) node equals to
dopt ¼
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
c
a
:
bða 1Þ
ð4Þ
860
B. Peng, A.H. Kemp / Computer Networks 55 (2011) 856–872
Proof. Consider a network G with a vertex (e.g. node) set
V = {v1, v2, . . ., vn} and edge (e.g. link) set E = {(vi, vj)} for
v i ; v j 2 R2 ; 1 6 i 6 n; 1 6 j 6 n. Here R2 is 2-dimensional
Euclidean space. The Euclidean distance from node vi to
vj dij = jvi vjj. Nodes in G are assumed to use continuously
variable transmission power (hence continuously variable
transmission range 0 < r 6 rmax) to communicate with
other nodes. The one-hop distance-energy efficiency
defined in [24] is:
e¼
progress
:
energy
ð5Þ
As shown in Fig. 1, dik is the distance between source
node vi and destination node vk. Node vj is a neighbour
node of vi with the distance dij and djk to vi and vk, respectively. Therefore, the problem is to maximize
ej ¼
dik djk
a
bdij þ c
ð6Þ
over the set
S ¼ ðdij ; djk Þ : dij > 0; djk > 0; dij þ djk P dik :
ð7Þ
v j0 is the projection of node vj on line vivk with the
0
distance dij and dj0 k to vi and vk, respectively. For 8v j 2 R2 ,
it is easily observed that:
e0j P ej :
ð8Þ
This means the optimal position must on the line of vivk.
Thus, the problem becomes to maximize (6) subject to
S ¼ ðdij ; djk Þ : dij > 0; djk > 0; dij þ djk ¼ dik :
ð9Þ
Taking the derivative of (6) with constraint in (9), setting it to zero, and solving for the optimal distance dij
results in:
dij ¼
node from those available, which gives the minimum total
energy consumption of a path. Several proposed energy
efficient routing algorithms give different methods to
select the best next relay.
Let v s ; v d 2 R2 be the source node and the destination
node, respectively. Let R2in and R2out be the portions of R2
containing the nodes whose distance from vs 6 dopt or
Pdopt, respectively. Only neighbours that are closer to the
destination than the current node are considered. The following algorithms are compared.
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
c
a
:
bða 1Þ
ð10Þ
h
Compared with optimal distance calculated in
[3,20,21,23], we conclude that the second approach gives
the identical optimal position as the first approach. For
the case of the power spent per unit of progress made, a
similar proof can be used to obtain the same conclusion,
which has been omitted here for brevity.
3.2. Energy-efficient geographic routing algorithms
Having obtained the optimal position for next node forwarding, the next question is how to select the next relay
j
d ij
i d opt p m
d jk
j'
k
Fig. 1. The optimal transmission range of the power-saving routing
algorithm.
Bounded Distance from Above [28]: At any hop, if vd is in
R2in then transmit to vd directly, otherwise pick as the
next relay the node in R2out that is closest to vs.
Bounded Distance from Below [28]: At any hop, if vd is in
R2in then transmit to vd directly, otherwise pick as the
next relay the node in R2in that is furthest from vs. If
no such node exists, apply Bounded Distance from
Above algorithm.
Geographic Random Forwarding (GeRaF) [29]: At any hop,
pick as the next relay the node that is closest to the destination, among those within a circle with center in vs
and radius dopt. If no such node exists, apply Bounded
Distance from Above algorithm.
Power Algorithm [3]: At any hop, consider the line from
the current relay to the destination, pick the point on
this line at a distance dopt from the current relay. Transmit to vd directly if dsd 6 (c/(b(1 21a)))1/a, otherwise
(that is, when dsd > (c/(b(1 21a)))1/a), choose as the
next hop the node which is closest to that point.
Greedy Minimum Energy: At any hop, pick as the next
relay the node in R2 that is closest to vs.
It is worth pointing out that GeRaF is an integrated
MAC/routing protocol. It is a receiver initiated protocol in
which nodes nominate themselves as potential relays,
depending on their geographic position and power availability. Since our comparison here focuses on routing performance, we omit the complex mechanism associated
with MAC layer and only present the related routing operation in above description of GeRaF.
The performance evaluation is presented in Figs. 2–4,
which compare the energy and hop count performance of
each routing algorithm listed for three different propagation loss exponents. The network used in the simulation
is a 300 m by 300 m field. Other than the source and destination, which are fixed at the point (0, 0) and the opposite
corner of the network with 330 m separation, all nodes are
uniformly and randomly placed. We use eelec = 50 nJ/bit
and b = 100 pJ/bit/m2 as in [27]. The traffic flow generated
at the source is 100 kbps. We assume all nodes use their
maximum transmission range to discover their neighbours,
then adjust transmission range appropriately between 0
and rmax (which equals 60 m in this scenario) with a radial
disk model of connectivity. Since the primary interest is
the routing performance, MAC layer effects such as collision and interference are not modelled here.
With reference to Fig. 2(a), The energy consumption of
all compared algorithms is relatively high when node density is low, and decreases rapidly as the number of nodes is
increased. All the algorithms can only relay via the limited
861
B. Peng, A.H. Kemp / Computer Networks 55 (2011) 856–872
0.7
4.5
Bound Distance from Above
Bounded Distance from Below
GeRaF
Greedy Minimum Energy
Power Algorithm
Total path power [Watt]
0.6
0.55
Bound Distance from Above
Bounded Distance from Below
GeRaF
Greedy Minimum Energy
Power Algorithm
4
Total path power [Watt]
0.65
0.5
0.45
0.4
0.35
3.5
3
2.5
2
0.3
1.5
0.25
0.2
0
100
200
300
Number of nodes in network
400
1
100
500
150
200
250
300
350
400
Number of nodes in network
450
500
450
500
(a) Total path power versus number of nodes in the network
60
50
Bounded Distance from Above
Bounded distance from Below
GeRaF
Greedy Minimum Energy
Power Algorithm
45
40
40
Number of hops
Number of hops
50
30
20
Bounded Distance from Above
Bounded Distance from Below
GeRaF
Greedy Minimum Energy
Power Algorithm
35
30
25
10
0
20
0
100
200
300
Number of nodes in network
400
500
15
100
150
200
250
300
350
400
Number of nodes in network
(b) Number of hops versus number of nodes in the network
Fig. 2. Performance evaluation of energy-efficient routing algorithms
with a = 2, eelec = 50 nJ/bit and b = 100 pJ/bit/m2.
number of nodes available in the network, and this leads to
longer transmission range than the optimal distance (in
the case of a = 2, dopt equals to 31.6 m from Eq. (10)), consequently they consume more energy. The Greedy Minimum Energy algorithm performs as well as other
algorithms until the increase in the number of nodes in
the network causes the average hop length to be shorter
than dopt. After this point, the greedy minimum energy
curve begins to diverge significantly from other algorithms
because it chooses hops that are individually cheapest,
while not considering total path cost. Therefore, its overall
energy consumption increase linearly with the number of
nodes. This trend can also be observed from the consistently increasing hopcount in Fig. 2(b).
The two ‘‘Bounded Distance’’ algorithms [28], which
were originally proposed for underwater acoustic networks, only show average performance in radio networks.
When the node density is low, the Bounded Distance from
Below algorithm outperforms the Bounded Distance from
Above algorithm in terms of energy consumption. While,
Fig. 3. Performance evaluation of energy-efficient routing algorithms
with a = 3, eelec = 50 nJ/bit and b = 100 pJ/bit/m2.
when networks become increasingly dense, the relative
performance is then reversed. This is because lower density networks only have a limited number of nodes available to choose from. Therefore, most transmission range
is longer than the optimal distance. In this case, preferring
the nearer nodes rather than the more distant node enables the Bounded Distance from Below algorithm to outperform the Bounded Distance from Above algorithm.
However, when the network becomes dense, the Bounded
Distance from Above algorithm shows better energy consumptions because a longer rather than a shorter hop is
preferred. The only difference between GeRaF and the
Bounded Distance from Below algorithm is that GeRaF
picks the next relay node which is closest to the destination instead of the one farthest from the source. This
guarantees the maximum advancement towards the destination within the coverage range of dopt. It is shown in
Fig. 2(a) that this difference gains GeRaF a significant
advantage over the Bounded Distance from Below
algorithm. When the number of nodes increases, GeRaF
862
B. Peng, A.H. Kemp / Computer Networks 55 (2011) 856–872
150
Total path power [Watt]
Bounded Distance from Above
Bounded Distance from Below
GeRaF
Greedy Minimum Energy
Power Algorithm
100
50
0
100
200
300
400
500
600
Number of nodes in network
60
55
Number of hops
50
Fig. 5. The expected distance of node j to the circle of node i which
achieves the minimum power consumption.
4. Analysis of the effect of location errors on
energy-efficient geographic routing
Bounded Distance from Above
Bounded Distance from Below
GeRaF
Greedy Minimum Energy
Power Algorithm
In this section, we provide a theoretical model of location errors and investigate the impact of the location error
on energy-efficient geographic routing. As discussed before, location errors not only affect the packet delivery ratio, but also consume extra transmit energy. The goal of
energy-efficient routing is to select the best relay node to
achieve energy saving. Therefore, we will show that it is
important to account for the impact of location error on
the performance of energy-efficient geographic routing.
45
40
35
30
25
20
15
100
4.1. Error model
200
300
400
Number of nodes in network
500
600
Fig. 4. Performance evaluation of energy-efficient routing algorithms
with a = 4, eelec = 50 nJ/bit and b = 100 pJ/bit/m2.
eventually reaches the energy performance achieved by
the Power Algorithm. The Power Algorithm achieves best
energy performance among all the compared algorithms.
This is also apparent in Fig. 2(b) in terms of hop count,
which remains on 10 hops. This is the optimal hop count
from source to destination. Therefore, comparing Fig. 2(a)
and (b), it can be observed that the hop count of the
algorithm which gives better energy performance is closer
to 10 hops.
The results for a = 3 and a = 4 in Figs. 3 and 4 also confirm that Power Algorithm achieves the best performance
in terms of energy consumption among all the compared
routing algorithms. However, it is worth noting that the
difference of the energy performance among the compared
algorithms becomes less when the propagation loss exponent increases.
In summary, the Power Algorithm is observed to have
the best performance in terms of energy consumption
among all the compared routing algorithms when perfect
location information is assumed.
Numerous previous work in the localization field (e.g.
[30–32]) has studied the sources of errors (such as the
accuracy of measurements, network density, uncertainties
in anchor locations, etc.) which impact localization, and
found that all these factors contribute to the final error in
a location estimate.
To provide a generic idea of localization errors, Gaussian errors are introduced to the x and y coordinates on
the real location of a node, with zero mean and finite standard deviation [29]. We assume that the location errors for
all nodes in a network are independent and the variance of
Gaussian error on x-axis and y-axis for each individual
node are equal. As shown in Fig. 5,2 node vi and node vj
are placed on a two-dimensional x–y coordinate plane with
real location Pi(Xi, Yi), Pj(Xj, Yj) and measured location
P0i ðxi ; yi Þ; P0j ðxj ; yj Þ, respectively. These can be expressed as
Xi = xi + Wi, Yi = yi + Wi, Xj = xj + Wj, Yj = yj + Wj, where
W i Nð0; r2i Þ and W j Nð0; r2j Þ are Gaussian random variables with zero mean and standard deviation ri and rj for
node vi and vj, respectively. Hence, the location error of
the node vj, which is the distance between its real location
and measured location, is calculated as
2
For simplicity, we assign source node vi to be at the origin and
destination node vk to be on the x-axis, and both without errors in the
figure. For the analysis and simulation, we assume that the location
information of all nodes has errors.
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B. Peng, A.H. Kemp / Computer Networks 55 (2011) 856–872
Dj ¼
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðX j xj Þ2 þ ðY j yj Þ2 ¼ W 2j þ W 2j ;
ð11Þ
Measured position
which follows a Rayleigh distribution [33] with probability
density function as
Dj
f ðDj Þ ¼
r
2
j
D2j =2r2j
e
A
ð12Þ
:
B
Let node vj be a neighbour of node vi. The probability
density function of the real distance between two nodes
vi and vj, f(Dij), follows a Rician distribution as [33]:
f ðDij Þ ¼
Dij e
Real position
A
ðD2ij þg2ij Þ=2r2ij
r2ij
I0
Dij gij
r2ij
;
E
E
S
d optM
radj
ð13Þ
rmax
C
C
B
F
F
D
G
G
where
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ðxi xj Þ2 þ ðyi yj Þ2 ;
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
¼ r2i þ r2j
gij ¼
ð14Þ
rij
ð15Þ
Fig. 6. Examples of the impacts of location errors.
and
I0 ðxÞ ¼
1
Z p
p
0
ex cos h dh
ð16Þ
is the modified Bessel function of the first kind and zeroth
order.
4.2. Analysis of the impacts of location errors
Previous work in [8,18] assume that all links between
neighbour nodes are symmetrical, namely a node is a
neighbour of the other node if and only if the other node
is located within the transmission radius of the node. In
practice, sensor nodes may have irregular propagation patterns, hence, this leads to asymmetrical links between
neighbours. Moreover, even if asymmetrical links could
be eliminated, e.g. via three-way handshake protocol, the
location errors may still affect the actual data transmission
when variable transmission range is used. In this case, the
transmission range is adjusted based on the distance between the sender and next forwarding node. Hence, location errors are recognized to have following three
impacts on energy-efficient geographic routing:
it impacts the border of the forwarding region;
It impacts the selection of next relay;
It impacts the actual transmission from the current
node to the next relay when variable transmission
range is used.
As illustrated in Fig. 6, S is the source node and D is the
destination node, when a node is actually located in the
forwarding area (shaded region) but the sending node believes it is outside, so decided not to forward packet (e.g.
node A), this will possibly cause a false local minimum
and probably transmission failure (if no recovery method
is used), especially for low network density. Even if a
recovery methods is used, it costs unnecessary energy consumption. On the other hand, if a node is located out of the
forwarding region, but the sender believes it is inside, and
therefore decides to forward a packet, this will cause back-
ward progress on the near side of the forwarding region
(e.g. node B). It has been concluded in [10] that the probability of backward progress increases when the standard
deviation of location errors, rij increases. When rij is fixed
and the chosen node is closer to the sender, the backward
progress probability increases. If we take the irregular
propagation pattern into consideration, this will cause
transmission failure even using maximal transmission
range, rmax, on the far side of the forwarding region (e.g.
node C). Beside the scenarios discussed above which are
all about the impact of location error on the nodes located
near the edge of the forwarding region, the location inaccuracy will also affect the selection of the next optimal relay
node. Consequently, a sub-optimal node could be selected
(e.g. node E) and lead to more energy consumption when a
better choice exists (e.g. node F).
The same simulation scenario from Section 3.2 is also
used here to validate the effect of introduced location errors on the previously discussed routing algorithms. In
addition, the location error is introduced by generating a
Gaussian distributed random variable Wi for both xi and
yi on node i, where W i Nð0; r2i Þ. Hence, by selecting ri,
we can generate a location error with desired deviation value. The location error deviation used here is 9 m for all
algorithms.3
Fig. 7 compares the total path power for an increasing
number of nodes in the network. As expected, the performance of all the routing algorithms are degraded by location errors, consuming more energy than when they
perform without errors. The reason is obvious that the
selection of the sub-optimal node leads to increased power
consumption. Notably, the Power Algorithm still outperforms all other algorithms due to the lowest increased
power caused by location error in Fig. 7. This can also be
observed from the different gradients for the algorithms
in Fig. 8, which plots the energy consumption versus the
standard deviation of location errors with 200 nodes in
3
Nine meters is arbitrarily chosen as 15% of the maximum transmission
range in this scenario to give an impression of the impact on performance.
864
B. Peng, A.H. Kemp / Computer Networks 55 (2011) 856–872
0.7
0.55
0.5
One−hop tansmission failure probability [%]
0.6
Total path power [Watt]
80
Bounded from Above
Bounded Above with errors
Bounded from Below
Bounded Below with errors
GeRaF
GeRaF with errors
GreMinEngy
GreMinEngy with errors
Power Algo
Power Algo with errors
0.65
0.45
0.4
0.35
0.3
0.25
0.2
0
100
200
300
Number of nodes in network
400
500
Fig. 7. Total path energy versus number of nodes in the network with
error deviation equals to 9 m.
70
60
50
40
30
20
10
0
Greedy forwarding
Power adjusting forwarding
0
0.2
0.4
0.6
0.8
Normalized standard deviation of location errors
1
Fig. 9. One-hop transmission failure probabilities versus the standard
deviation of location errors for greedy forwarding g = 0.8r and powersaving routing algorithm g = r.
0.65
0.55
Total path power [Watt]
where ri is the transmission range of node i, Dij is the real
distance between node i and node j, rij is the standard
deviation, and Q1 is Marcum’s Q function with m = 1 [33].
In the case of the power-efficient algorithm, the transmission range ri will be set to gij. Hence, the transmission failure probability becomes
Bounded from Above
Bounded from Below
Power Algorithm
GeRaF
GreMinEngy
0.6
0.5
0.45
gij gij
:
Pr r adj < Dij ¼ Q 1
;
0.4
rij rij
0.35
0.3
0.25
0.2
0
5
10
15
20
25
30
Standard deviation of location errors [%]
35
40
Fig. 8. Total path power versus the standard deviation of location errors
with 200 nodes.
the network. In summary, by comparing the power consumption of the routing algorithms in the presence of location errors, the Power Algorithm is shown to have the least
impact from location errors, therefore, it achieves the best
power performance. This is the main reason that the Power
Algorithm will be used as the basis to develop our proposal
in the next section.
Beside the impact of location error on node selection, it
will also impact the actual transmissions when variable
transmission range is used. After a node is selected as the
next relay node, the sender will adjust its transmission
range based on the measured distance between the two
nodes, and then transmit the packet. If the measured distance is longer than the real distance between the two
nodes, it will simply consume excess energy. However, if
the measured distance is shorter than the real distance,
the transmission will fail (e.g. node G).
It has been given in [10] that the probability that a
packet transmission from node i to node j fails as:
gij ri
;
Pr Dij > ri ¼ Q 1
;
rij rij
ð17Þ
ð18Þ
As expected, this shares the property described in [10],
that the transmission failure probability increases as the
standard deviation of location errors rij increases. Moreover, since the transmission range in the power-saving
algorithm will be adjusted to only reach the estimated position of node j, i.e. the estimated position of node j will be
right on the edge of the transmission range (node G in
Fig. 6), the transmission failure probability will be much
higher than described in [10] where the transmission
range, r is fixed. Fig. 9 shows the relationship between
one-hop transmission failure probability and the standard
deviation of the location error for both normal Greedy Forwarding (when g = 0.8r) and the Power Algorithm (g = r).
For the same standard deviation of location error, the
transmission failure probability of the power-efficient
routing algorithm is much higher than for the normal
Greedy Forwarding algorithm. Even for small variance of
location error, the failure probability for the Power Algorithm reaches 50%. This confirms our expectation that energy-efficient routing algorithms which use adjustable
transmission range suffer from significant packet loss
when location errors exist. Table 1 summaries all the impacts of the location errors and their consequences.
5. Energy efficient geographic routing algorithm in the
presence of location errors
The previous section has shown that location errors
have a significant impact on existing energy efficient
geographic routing algorithms in terms of both packet
delivery rate and energy efficiency. In this section, a novel
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B. Peng, A.H. Kemp / Computer Networks 55 (2011) 856–872
Table 1
Summary of the impacts of the location errors on energy-efficient
geographic routing.
Impact of location
errors
Examples (Fig. 6)
Results
Transmission
failure
Backward progress
Node C and G
Lost packets
Node B
False local
minimum
Node A
Sub-optimal relay
Node E instead of
node F
Routing loops,
increased energy
consumption
Wrongly enter into the
recovery process and
increased energy
consumption
Increased energy
consumption
5.1. Objective function
As shown in Fig. 5, it is assumed that source node vi is
measured as being located at the origin. From the analysis in Section 3, the location that achieves minimum
power consumption (Pm in Fig. 5) is located in line with
source node vi and destination node vk with the distance
dopt from the source node. Since the coordinates of node
vi are Gaussian random variables, the real position of m,
Pm, with respect to node i, is also a Gaussian random variable with mean P 0m (dopt, 0) and standard deviation
rm = ri. Our objective is to find a next forwarding node
vj, whose real location is closest to position Pm among
all neighbours, hence, we define the objective function
as follows:
Y j ðDÞ ¼ E½Djm ;
geographic routing scheme is proposed to address those
effects in the presence of location errors. More specifically,
our proposal minimises the impact of location errors on
energy efficiency due to the selection of sub-optimal relay
and the packet delivery rate caused by transmission failure
from variable radio range adjustment. Improved accuracy
of relay selection (hence more energy efficiency) is
achieved by using the expected value of the distance between the optimal point and the neighbours. Transmission
failure cause by errors is addressed by combining an
adaptive transmission strategy with the proposed routing
algorithm. Since the Power Algorithm outperforms all the
other existing routing algorithms discussed in Section
3.2, it is used as the basis to develop our proposal. Notably,
since the existing energy efficient geographic routing
algorithms discussed in Section 3.2 only vary in the way
of how to select the best relay with respect to the optimal
position, the approach used in our proposal can also be
applied to other energy efficient geographic routing
algorithms.
All nodes in the network are assumed to be able to vary
their own transmission range (by adjusting transmit
power) and have the same fixed maximum range, rmax P
dopt. Since each node measures its own location and estimates its own error characteristic, an error information
field is inserted in the header of geographic routing messages to broadcast the statistical characteristics of location
error (e.g. mean and standard deviation) to neighbours. The
location information and related error characteristics of the
destination can be obtained by location service protocols.
Regarding localization algorithm (e.g. [34]), such error statistics can be obtained from the localization process. There
exists a quality figure associated with each node to estimate the quality of the location estimation. Details of
how to calculate this quality figure vary among different
localization algorithms and the value is also related to
deployment environment, such as the number of available
anchor nodes and Dilution of Precision (DOP), etc. Here,
we do not discuss this quality figure in detail and it is assumed available to our routing algorithm. The interested
reader is referred to an extensive survey of localization in
[35]. Moreover, location inconsistency is not considered,
hence the location information received by all nodes is
identical.
ð19Þ
where Djm denotes the real distance between neighbour
node j and position Pm. Since Djm is also a random variable
following a Rician distribution as defined in (13), the
expectation
rffiffiffiffi
EðDjm Þ ¼ rjm
p
2
L1=2
!
g2jm
2 ;
2rjm
ð20Þ
where
h
x
xi
xI1
:
L1=2 ðxÞ ¼ ex=2 ð1 xÞI0
2
2
ð21Þ
Yj(D) is defined as the expected distance of node vj from
location Pm which achieves the minimum power consumption between source and destination node. By calculating
the value of Yj(D) using the measured position and error
deviation of each node, the current node will select a next
forwarding node which has the Least Expected Distance
(LED) from the location Pm. Therefore, the LED algorithm
is able to select a node which statistically achieves minimum total path energy consumption in the presence of
location errors. Our LED algorithm can be formalized as
follows:
LED (s,k)
j
s
do
i
j
if Did 6 (c/(b(121a))) 1/a
then choose node k
otherwise Let j be neighbour of i that
minimizes Yj(D) = E[Djm]
Send packet to j
until j = k (destination k reached)
Here, Djm denotes the real distance between neighbour
node vj and the position of M.
Fig. 10 illustrates how the objective function Yj(D) of the
proposed algorithm LED varies with the standard deviation
of location errors for three fixed values of measured distance gjm. Generally, Yj(D) increases monotonically as the
standard deviation of location error increases. Therefore,
the LED algorithm will prefer the node with smaller standard deviation of error. Moreover, among the three curves
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B. Peng, A.H. Kemp / Computer Networks 55 (2011) 856–872
5.2. Adaptive transmission strategy
Although the proposed LED algorithm is able to select
the next forwarding node which can statistically minimize
power consumption when location errors exist, once the
next node is determined, it still suffers from potential
transmission failure due to the variable transmission control (node G as analyzed in Section 4.2 with at least 50%
chance of packet loss in one-hop transmission). In this section, an adaptive transmission range control scheme is proposed to address this problem. From the analysis in Section
4.2, the end-to-end PDR for a path length of Nhops can be
expressed as
Nhops
PDR ¼
Y
Y
gij ri
;
1 Q1
;
N hops
ð1 Prfr i < Z ij gÞ ¼
i;j¼1
i;j¼1
rij rij
ð22Þ
Fig. 10. Yj(D) versus rjm.
where
which represent three different values of estimated distance from node vj to position P0m , the curve with gjm equal
to 0 achieves the least value for all the r compared with
gjm equal to 2.5 and 5. This is obvious because when
gjm = 0 the estimated position of this node is actually in
the optimal position. It is worth noting that the difference
of the Yj(D) value between gjm = 0 and gjm = 2.5 is larger
when r is small, and such difference decrease when r increases. The reason is that bigger r increases its impact
on the value of Yj(D), consequently, reduce the weight
gjm on the function. Therefore, it is illustrated that our
objective function Y(D) takes consideration of both g and
r of neighbour nodes to select an optimum candidate.
Fig. 11 shows the relationship between the objective function Yj(D) with the estimated distance from neighbour
node vj to the position P0m for three fixed values of standard
deviation of errors. The minimum value of Yj(D) is achieved
when the estimated distance is 0. Hence, this confirms that
our LED algorithm prefers the node closest to the minimum power position, and therefore achieves the optimized
energy consumption in the presence of location errors.
Fig. 11. Yj(D) versus gjm.
gij 6 ri 6 rmax :
ð23Þ
We also define the extended transmission range of node i
as r ext
¼ ri gij , and therefore, the associated extra energy
i
consumption of the path is
Nhops
ENhop ¼
X
a
ðbðr ext
i Þ þ cÞ
ð24Þ
i¼1
Once a node is chosen by the LED algorithm, instead of
adjusting the sender’s transmission range to the exact distance between the sender and the chosen node, the transmission range is increased by a margin rext. For a given
error environment, a longer transmission range reduces
the transmission failure probability. Therefore, this scheme
tries to increase the transmit power (hence the transmit
range) to cover the number of standard deviations of estimated location errors to compensate for the location errors
and save transmission failure. Fig. 12 shows how PDR increases by increasing normalized extended transmission
range, rext for a path consisting of 20 hops. Here, we assume
Fig. 12. PDR versus normalized extended transmission range of 3 fixed
sigma through a path of 20 hops.
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B. Peng, A.H. Kemp / Computer Networks 55 (2011) 856–872
Fig. 13. PDR versus normalized standard deviation of 3 fixed extended
transmission range through a path of 20 hops.
that all the relay nodes along the path have the same standard deviation of location error r = 0.1, 0.2, 0.3, respectively. For relatively small location errors (r = 0.1), 30%
transmission extension can improve PDR significantly to
more than 90%. However, when the standard deviation increases to r = 0.3, the same transmission extension results
in less than 10% PDR. To have a satisfactory PDR in this
case, a longer transmission extension has to be used.
The next question is how to determine an appropriate
the length of the margin rext. Larger rext leads to higher energy consumption along a path, but on the other hand, improves PDR. Naturally, rext could be increased adaptively
depending on the standard deviation of the location error
rij of the chosen node. Since the LED algorithm guarantees
the standard deviation of location error of the chosen node
is minimum among all neighbours, this adaptive transmission strategy for the chosen node guarantees that the total
transmission range will be kept to a minimum. Hence, the
power consumption is minimized. By extending the transmission range ri for each relay node along a path, the PDR
obtained for rext = r, 2r and 3r are plotted in Fig. 13. Compared with the range rext = r, the PDR are significantly improved by increasing the transmission range by 2r. For
rext = 3r, the PDR consistently remains above 90% through
all the standard deviations of location errors in Fig. 13.
Although this improvement of PDR is achieved by sacrificing extra transmission power, we will show in the next
section through simulation results that thanks to the combination of the adaptive feature of the transmission strategy and the LED algorithm, the extra energy consumed
for the extended transmission is not significant compared
to the total path energy consumption.
6. Simulation evaluation
To better understand the impact of various network
parameters on our proposal, a detailed simulation study
was carried out in Matlab to verify the performance of
LED by comparison with Power Algorithm in the presence
of location errors. Since we are mostly interested in the
routing performance, MAC layer effects such as collisions
and interference were not modelled.
The simulated network supports localized broadcast
packets and packets are simply delivered to the neighbours
within the radio transmission range (circle) from the sending node. A more realistic link model should take radio
propagation effects into account and this is to be included
in future work. In the following simulations, a static and
stable sensor network (i.e. no mobility and no failures)
without obstacles and with nodes having accurate radio
ranges is assumed. With the exception of source and destination nodes which are set to the diagonal corners of the
network, all other nodes are uniformly and randomly
placed within a field for each iteration. Randomly generated Gaussian distributed location errors with zero mean
and given standard deviation r are added in the real location coordinates as measured location coordinates. Then
the Power Algorithm and LED are evaluated on the same
network with the same error characteristic for each iteration. Disconnected networks which are generated are not
used. To allow for easy comparison between different scenarios, location errors are normalized to the radio range
(i.e. r, the standard deviation of location error, is expressed
as a percentage of the transmission range).
We assume all nodes use their maximum transmission
range to discover their neighbours, then adjust the transmission range appropriately between 0 and rmax with a
radial disk model of connectivity. The same power consumption model from Section 3 is adopted with parameters eelec = 50 nJ/bit and b = 100 pJ/bit/m2. In the case of a
network void or dead end, the forwarding packet will be
dropped, and the transmission is recorded as failed. In
the literature, this problem can be addressed in a number
of ways, however, it is not the focus of this preliminary
study and is left for future work. The traffic flow generated
at the source is 100 kbps. As discussed in the previous sections, location errors not only have an impact on the stage
of node selection but also on the transmission, hence these
two stage are simulated as follows. Three scenarios to be
investigated are illustrated in Table 2. To account for the
randomness in generating topologies and location errors,
each simulation is repeated with a different seed, and the
results are the average of 100 iterations.
First, two algorithms: the Power Algorithm and LED
algorithm are compared. Since the main focus is to evaluate the power consumption at the node selection stage of
the two algorithms, we initially assume there is no transmission failure. We use the performance of the Power
Algorithm with perfect location information (i.e. no location errors) as a lower bound on the energy consumption
of both algorithms in the presence of location errors. The
first scenario is in a 500 m 500 m field, with free space
path loss exponent, a = 2. The same maximum transmisTable 2
Scenarios for simulation.
Scenario
Area (m2)
rmax (m)
r (%)
Nodes
a
1
2
3
500 500
100 100
50 50
60
20
10
0–50
0–50
0–40
100–800
50–500
150
2
4
4
B. Peng, A.H. Kemp / Computer Networks 55 (2011) 856–872
sion range of 60 m is used for all nodes in the network,
which is about twice of the optimal transmission range
of 31.6 m in this scenario. For the second scenario, we
use path loss exponent a = 4, which is typical for urban
propagation conditions. In this case, the optimal
transmission range is calculated as 4.28 m. Therefore, we
reduce the maximum transmission range to 20 m in this
scenario. Accordingly, the simulation field is reduced to
100 m 100 m.
Figs. 14(a) and 15(a) compare the power consumption
of the Power Algorithm and proposed LED algorithm for
increasing number of nodes. The standard deviation of
location error for each node is uniformly distributed in
the interval [0, 30%] of the maximum transmission range.
As can be seen, location errors impact on both algorithms,
and lead to a higher power consumption compared with
the Power Algorithm without error (in this idealised but
unrealistic situation). Compared with the Power Algorithm
with errors, the proposed LED algorithm achieves increased saving of power as the network density increases.
8
Power Algorithm without errors
Power Algorithm with errors
LED with errors
7
6
Power[Watt]
868
5
4
3
2
1
0
50
100
150
200 250 300 350
Number of nodes
400
450
500
18
Power Algorithm without errors
Power Algorithm with errors
LED with errors
16
14
0.7
Power Algorithm without errors
Power Algorithm with errors
LED with errors
Power [Watt]
12
Power[Watt]
0.65
10
8
6
0.6
4
0.55
2
0
0.5
200
300
400
500
Number of nodes
600
700
800
0.75
Power Algorithm without errors
Power Algorithm with errors
LED with errors
0.7
0.65
Power[Watt]
10
20
30
40
50
Standard Deviation of location error [%]
0.45
100
0.6
0.55
0.5
0.45
0
0
10
20
30
40
Standard deviation of location errors [%]
50
Fig. 14. The energy consumption comparison of the routing algorithms in
Scenario 1.
Fig. 15. The energy consumption comparison of the routing algorithms in
Scenario 2.
In Scenario 2, LED saves up to 50% of the energy compared
with the Power Algorithm. This is because at high densities, it is possible to minimize power consumption, due
to the large probability that a ‘‘very’’ optimal positioned
node exists. Hence, the LED algorithm more likely to select
a node which achieves minimum power consumption. This
also explains the reason the power consumption decreases
as the number of nodes increases for a fixed source and
destination pair in both Figs. 14(a) and 15(a).
The above results illustrate that our proposal achieves
better power saving when node density is high. This is
not surprise as a class of geographic routing algorithms
normally performs better in high node density networks.
Figs. 14(b) and 15(b) compare the power consumption
of both algorithms for increasing the location error by
varying the standard deviation of the error for each node
from 0% to 50% of the maximum transmission range. As expected, when there is no location error, the power consumption of the Power Algorithm is almost constant (the
little variation is due to randomly generated topologies).
869
B. Peng, A.H. Kemp / Computer Networks 55 (2011) 856–872
After validating the better power consumption performance of the proposed LED compared to the Power Algorithm in the node selection stage, now we turn our
attention to the impact of location errors on the actual
hop-to-hop transmission. By combination with the proposed adaptive transmission strategy, LED is expected to
achieve minimized power consumption while maintaining
an acceptable PDR in the presence of location errors.
Fig. 16 shows the PDR and power consumption of the
proposed LED algorithm with the adaptive transmission
strategy by varying the standard deviation of location errors from 0 to 40% of the maximum transmission range
in Scenario 1. The low PDR of just one r extended transmission range, as analyzed in Section 5.2, leads us to present the PDR of LED with 2r to 4r transmission extension in
Fig. 16(a). Tables 3 and 4 illustrate the end-to-end hopcounts under various range of location errors for all the
As the location error increases, the power consumption of
both algorithms increases since more routing are made under non-optimal route selections. However, since the LED
algorithm considers both measured location and the error
deviation of a node when selecting the next relay node, it
is able to statistically choose a next node which is nearer
to the best power saving point than the Power Algorithm.
Consequently, LED consistently consumes less power than
the Power Algorithm and saves a significant amount of
power (up to 15% in Scenario 1 and up to 75% in Scenario
2 when the location error is larger than 30%). Comparing
free space propagation in Scenario 1 (a = 2) with the typical urban propagation conditions of Scenario 2 (a = 4), the
higher power loss index leads to a significant increase of
the total path power consumption and the reduced dopt.
Hence, more hops are needed to relay a packet between
the same source/destination pair.
0.66
Power Algorithm without errors
Power Algorithm
LED without extension
LED with 2σ
LED with 3σ
LED with 4σ
0.64
Power consumption [Watt]
0.62
0.6
0.58
0.56
0.54
0.52
0.5
0.48
0
5
10
15
20
25
30
35
40
Standard deviation of location errors [%]
Fig. 16. The performance of LED routing algorithms with adaptive transmission in Scenario 1.
870
B. Peng, A.H. Kemp / Computer Networks 55 (2011) 856–872
compared algorithms in scenario 1 and scenario 3, respectively. Referring to the average hopcount of the simulated
routing algorithms in Table 3, we observed the similar
PDR in Fig. 16(a) with those in Fig. 13. Accordingly,
Fig. 16(b) illustrates the corresponding power consumption on a path and the extra power used to extend the
transmission range from 2r to 4r. It can be inferred from
Fig. 16(a) and (b) that even with 4r transmission extension, which enables the PDR to reach nearly 100% across
all error deviations, the power consumed by this extension
is not significant (less than 10% of the total consumption
on a path). In addition, Fig. 16(c) compares the total power
consumption of the Power Algorithm and the LED algorithm with the three transmission extensions by increasing
location errors. It is observed that the LED with transmissions extension of 3 or 4r only consumes minor extra energy compared with the Power Algorithm, while, it is able
to offer high PDR as shown in Fig. 16(a). This is because the
location error on the node selected by LED algorithm has
been minimized, and hence the extension of the transmission range (i.e. extra power consumption) for the chosen
node is also minimized. Therefore, the combination of
LED and the adaptive transmission strategy is able to
maintain the required PDR in the presence of location errors with minimum power consumption.
Fig. 17 shows the same simulation evaluation as above,
but in a smaller field with reduced maximum transmission
range for each node in a larger path loss propagation environment as described in scenario 3 in Table 2. Since the
hopcount from source to destination is reduced in this scenario as shown in Table 4, the observed PDR is higher in
Fig. 17(a) than Fig. 16(a). It is observed in Fig. 17(b) that
the extra power used to extend the transmission range
from 2r to 4r increases rapidly when the standard deviation of location errors increases. This is not surprising due
Table 3
Average number of hops in Scenario 1.
a
b
r (%)
PAa
PA w.e.b
LED 2r
LED 3r
LED 4r
0
8
16
24
32
40
22.34
22.59
22.77
22.17
22.34
22.26
22.26
22.21
22.44
22.02
22.06
21.96
22.77
22.06
22.44
22.27
21.79
21.57
22.17
21.91
22.24
21.99
22.02
22.01
22.59
22.34
22.37
21.94
21.86
21.99
Denote Power Algorithm.
Denote Power Algorithm with location errors.
Table 4
Average Number of Hops in Scenario 3
a
b
r (%)
PAa
PA w.e.b
LED 2r
LED 3r
LED 4r
0
10
20
30
40
16.27
16.14
16.21
15.93
16.27
16.21
15.80
15.94
15.70
15.48
16.21
15.78
15.88
15.20
15.61
15.93
15.90
15.61
15.48
15.48
16.14
15.76
15.82
15.30
15.34
Denotes the Power Algorithm.
Denotes the Power Algorithm with location errors.
to the larger path loss exponent in this scenario. However,
for relatively small location errors (less than 30%), the extra power consumption is still in the range of 10% of total
path power consumption for 4r. Finally, Fig. 17(c) confirms
the power efficiency of LED with transmission extension by
comparing with the Power Algorithm in this scenario.
The results of simulations with scenario 2 confirm the
qualitative behaviour just described, and are therefore
omitted due to space considerations.
In summary, the proposed LED algorithm with adaptive
transmission strategy is able to achieve improved end-toend PDR, while at the same time, maintain the approximately low power consumption compared with the Power
Algorithm. The combination of the adaptive feature of the
transmission strategy and LED algorithm guarantee the extended range of the chosen node (hence, the extra power
consumption for the extension) to be minimum among
all neighbour nodes. However, how to determine the value
of the extension is a trade-off between PDR and power consumption. Therefore, there is no optimum value of the
extension in general, and it depends on the particular network scenario and requirements for PDR and power
consumption.
7. Conclusion
Power efficient geographical routing has been shown to
reduce energy consumption and prolong the lifetime of
multi-hop wireless networks. However, in practical
deployment scenarios where location inaccuracy will inevitably exist, these routing algorithms are vulnerable to
location errors. This leads to a substantial performance
degradation in terms of energy consumption. This paper,
first analyzes the optimal distance of the power saving
geographic routing algorithm and proves that the optimal
forwarding position which the two different approaches
calculate, to achieve best total path power saving per packet, is identical. This insight is then used to compare a class
of existing power efficient geographical routing algorithms
in an error free environment. After introducing the error
model, the impact of location errors on geographic routing
is investigated. By incorporating location errors into an
objective function, a novel power-saving geographic routing algorithm named LED is proposed. It selects the next
forwarding node which can maximize the probability to
achieve minimum power consumption, and therefore,
exhibits large energy savings compared to other routing
algorithms. An adaptive transmission strategy is then proposed to cope with the transmission failure caused by location errors. Finally, extensive simulation results provide
insights into the performance of our proposal under different conditions and confirm that our proposed routing
strategy achieves higher energy efficiency as compared to
other schemes.
This study represents an important step in understanding and designing energy efficient geographic routing as
well as localization algorithms in multi-hop wireless networks under complex error environments. It was observed
in the simulation that the proposed LED routing algorithm
showed better performance especially when node density
871
B. Peng, A.H. Kemp / Computer Networks 55 (2011) 856–872
1
Power Algorithm without errors
Power Algorithm
LED without extension
LED with 2σ
LED with 3σ
LED with 4σ
Power consumption [Watt]
0.9
0.8
0.7
0.6
0.5
0.4
0
5
10
15
20
25
30
Standard deviation of location errors [%]
35
40
Fig. 17. The performance of LED routing algorithms with adaptive transmission in Scenario 3.
is high. Hence, it is suggested that LED could be more suitable for those WSN applications which consist of a large
number of sensor nodes. The focus of this paper was to
minimise energy consumption during delivery of a single
packet from source to destination. The issue of maximising
overall network lifetime can be jointly optimized with our
proposals to balance the network load and energy consumptions. How the performance of these combined
mechanisms would act is an interesting problem to be further investigated. There are a number of applications in
WSNs which have both delay and energy constraints. Future research is needed to exploit the inter-relationship between a power-efficient metric and an average delay
metric through integrating this work with MAC and other
layer protocols.
Acknowledgments
This research is partially supported by the Overseas Research Students grant of the Secretary of State for Education and Science, UKand the University of Leeds Tetley
and Lupton Scholarship. We also thank the anonymous
reviewers for their comments and suggestions to improve
the quality of this paper.
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Bo Peng received a BSc from Xidian University, Xi’an, China, in 2002 and MPhil from
University of Leeds, UK, in 2006, both in
Electronic and Electrical Engineering. He was
then awarded an ORS scholarship to pursue
his PhD in the School of Electronic and Electrical Engineering, University of Leeds. From
2006 to 2007, he worked for the CAA Institute
of Satellite Navigation, University of Leeds
investigating reliable positioning in wireless
sensor networks for an EPSRC project. His
research interests are in the wireless communication and networking area with a focus on geographic routing,
quality of service and positioning.
Andrew H. Kemp received a BSc from the
University of York, UK, in 1984 and after a
period in industry, a PhD from the University
of Hull, UK, in 1991. His doctoral studies
investigated the use of complementary
sequences in multi-functional architectures
for use in CDMA systems. He spent several
years working in Libya and South Africa
assisting in seismic exploration and worked at
the University of Bradford as a research
assistant investigating the use of Blum, Blum
and Shub sequences for cryptographically
secure 3rd generation systems. More recently he helped develop wireless
fieldbus systems for industrial sites and has been lecturing at the University of Leeds, UK in communications for the last 10 years. He has over
50 scientific journal and conference papers and a book chapter published.
His research interests are in localization for WSNs, routing, multipath
propagation studies to assist system development and wireless broadband connection to computer networks incorporating quality of service
provision. He is a member of the IEEE, the IET, and a Fellow of the Higher
Education Academy.