Positioning of Relay Stations in Enhancing Lifetime of an Energy
Constrained Two Tiered Wireless Sensor Network
B. Paul, Ifte Khairul Amin
Department of Electrical and Electronic Engineering
Shahjalal University of Science and Technology
Kumargaon, Sylhet-3114.
Bangladesh.
{[email protected],[email protected]}1, [email protected]
Abstract :- Depletion of energy of any of the CHs (cluster heads) in a two tiered wireless sensor network
informs us about the lack of network coverage and failure to provide full coverage defines the end of
network lifetime. From literature we come to know that, center of a minimum enclosing circle that
encloses all the CHs is the optimal position for BS(base station) in case of a static network or sink in case
of a dynamic network in an energy constrained WSN(wireless sensor network). Accepting the fact just
described, the presence of a disperse node(s) can drastically reduce network lifetime. In this paper, we
provide mathematical analysis that depicts how the dispersive nature of node distribution affect network
lifetime. The deliberate use of relay stations can improve network lifetime which is justified by simulation
results.
Key-Words:- Wireless sensor network, Cluster head, base station, disperse node, sink, lifetime, relay
station.
1 Introduction
The easiness to deploy a WSN has drawn the
attention of researchers for a long time.
Responding to the queries and managing events
such as target tracking are two of the most
popular applications of a WSN among many. A
WSN is a network that contains several tiny
nodes which can perform a variety of operations.
The nodes are placed in such a way so that they
can cover certain regions of interest. The
processing of data is performed through the
cognitive knowledge of the nodes. The
collective result is then transmitted to a central
node known as a base station in case of a static
network and a sink in case of a dynamic
network. Since the nodes are driven by batteries
and considering typical application scenarios,
recharging the batteries is not considered a
feasible solution. The imbalance in the depletion
rate of energy of the nodes can hamper network
operation. Thus a significant effort is made to
overcome this imbalance in order to enhance
network lifetime.
Several tiny sensor nodes (SN) build up the
backbone of a sensor network. The type of
sensor nodes used in an application depends on
the application type. Sensor nodes are small
devices normally operated by batteries are
capable to collect data, process those data and
transmit the processed data to a predetermined
destination. A significant effort has been made
in recent years to develop protocols in order to
ensure successful operation of a sensor network.
In a dynamic network sometimes cognition
based data routing is also observed in our
studies. However, since the nodes are battery
driven a lot of concentration goes into saving
their energy while maintaining the required
operation. The amount of energy spent in the
process of data transmission and reception is
very high comparing to energy spent in other
processes.In physical layer a well-chosen BS co-
ordinate can reduce the amount of energy spent
and thus can enhance network lifetime.
Network lifetime, connectivity, coverage are
some of the design metrics for a typical WSN.
Sink
Macro sensor node
CH
Fig.1: A typical wireless sensor network architecture.
A variety of network topology is considered for
WSNs. A homogeneous network is the one
where all the nodes have similar energy and
perform almost similar type of works. On the
other hand, a heterogeneous network is the one
where some nodes have more energy comparing
to others, have higher data processing capability
and perform some additional responsibilities
comparing to other nodes in the network. A two
tiered network is the network where the
communication process is completed in two
stages. The whole region is divided in many
small regions. The general purpose nodes are
responsible to collect data and transmit those
data to the cluster head (CH). The cluster head is
the node selected from a group of nodes which
has more energy and much better data
processing capability comparing to other nodes.
The CHs are responsible to forward those data to
the base station or the sink.
Those design metrics arise from the fact that
WSN can be deployed to serve different types of
services. Some nodes might have to generate
and transmit data more frequently comparing to
others. As a result, those nodes can deplete their
energy at a faster rate comparing to others.
However, the death of some of the nodes will
not hamper the operation of the network if
enough nodes are alive to serve the purpose. On
the other hand, death of a CH can cut short the
network lifetime. A CH is responsible to
transmit the data generated in a particular
region. If any of the CHs runs out of energy, it
would result in a loss of connectivity. For many
applications, this loss of connectivity defines the
end of network lifetime. Therefore, it is of prime
importance to make an effort to reduce the
amount depletion of energy of those CHs in
every possible way. In the physical layer, a wellchosen BSor sink position can prolong network
lifetime.In this paper, we focus on this issue and
emphasize on the optimal positioning of relay
stations as well in order to improve network
lifetime.
2 Relevant Works
The optimal position for a BS or a sink can be
obtained using optimization algorithms. Among
those algorithms the use of particle swarm
optimization is observed in [1-3]. Although it is
possible to fetch the correct output from a set of
given data using particle swarm optimization, it
fails to provide a good insight about this
particular problem. This limitation is overcome
in [4-7]. Those works suggest that, the center of
the minimum enclosing circle that encloses all
the CHs in a given topologyis the optimal
position for a BS. The importance of placing the
BS optimally in a WSN remains the focus in
[8,9] as well. However, the presence of disperse
CHs can dramatically reduce the network
lifetime which remains unfocussed in those
works. The impact of disperse CHs on network
lifetime is emphasized in [10]. A new design
scheme namely “LEDN” was proposed in this
paper. However, nothing much is discussed
about the positioning of those relay stations. In
this paper, we show that, the dispersive nature of
the network put constraints on positioning the
relay stations. Nevertheless, the optimal
positioning of those relay stations can
significantly increase network lifetime.The idea
of base station repositioning with the purpose of
enhancing network performance can be observed
in [11]. Optimal power scheduling, collaborative
beam forming or power consumption based load
sharing topologies are some other efforts in the
physical layer which are thought of with the aim
of enhancing network lifetime [12-14]. Some
applications of WSN are provided in [15-17].
3 Impact of a Disperse Node(s) on
Network Lifetime
A CH’s lifetime can be calculated as
𝐿(𝑖) =
𝑒(0)
𝑏
𝑟(𝑎1 +𝑎2 𝑑𝑖 ′ )
(1)
where 𝑖 is CH’s identity, 𝑟 is the data rate, 𝑎1 is a
distance independent parameter, 𝑎2 is distance
dependent parameter, 𝑑𝑖 ′ is the distance from the
CH to a destination CH or BS, 𝑏 is the path loss
exponent, typically ranges between 2 and 4
based on the type of environment and 𝑒(0) is the
initial energy of the CH. The lifetime of the
network is defined as
𝐿 = 𝑚𝑖𝑛 𝑖=1𝑛𝑙(𝑖)
(2)
Now consider a topology of CHs (T1) and its
calculated lifetime is L(T1).
The above
definition of lifetime dictates that the center of a
minimum enclosing circle with radius 𝑑1 is the
best location for the BS or sink regardless of the
presence of any disperse CHs (A dispersed CH
is the CH whose position is not in the proximity
of the majority CHs). Next we determine the
presence of any disperse CH in the network. In
case of the presence of disperse CH we consider
a virtual topology excluding the disperse CHs.
The reduction of network lifetime can be
calculated as
𝐿(𝑇2 ) − 𝐿(𝑇1 ) = 𝑑
2𝑘𝑑2 𝑑3 +𝑘𝑑3 2
3
2 2
2 +2𝑑2 𝑑3 +𝑑2 𝑑3
4
(3)
where, 𝑑2 is the radius of the minimum
enclosing circle for topology T2 and 𝑑3 = 𝑑1 −
𝑒(0)
𝑑2 and 𝑘 = 𝑟 . If more than one disperse CH
are present in the network the analysis and result
found for a single disperse CH remains same
since the farthest disperse CH will determine the
radius of second circle. Expression(1) dictates
that if 𝑑1 is the radius for L(T1) and 𝑑2 is the
radius for L(T2), a third circle is obtainable
taking the connecting line of the two centers of
first two circles and the points inside that circle
considered as the center of the enclosing circle
for topology T1 will enhance network lifetime.
4 Dispersive Nature of a Network
For a dynamic network, it is possible to obtain
the co-ordinates of the CHs using GPS tracking
device and for a fixed network the co-ordinates
of the CHs are determined by network designers
in accordance with the application requirements.
A detailed discussion on this issue can be
obtained from [18]. We observe the mean
average distance of the disperse CH from other
CHs in the network will deviate from the
remaining ( n  1) CHs. Using this observation,
we can find out the disperse CHs. The distance
between any two CHs can be calculated using
the
Euclidian
formulae,
d  ( x1  x2 ) 2  ( y1  y 2 ) 2 .For any CH in
T1 , we obtain a set of (n  1) members ; each
member representing the distance between the
CHs and some other CHs in the network, n CHs
give n sets each having ( n  1) members. The
mean value of a set can be found using the
following expression.
Mean m  The sum of the (n  1) values /( n  1)
Fig.2 Finding a disperse CH in a network
. As n sets give n mean values, we define a set S
of
n
mean
values,
Algorithm for disperse CH(s)
DisperseNodesAlgo
. Let M be the mean of the set S. We find the
variance (V) of the data set by expression (3)
1. Declare an array of n sets
Set S  m1 , m2 , m3 ..................mn2 , mn1 , mn 
V
 M)
N 1
 (X
2. Start Loop (1:n)
2
(3)
Where X represents the members of set S and n
represents the total number of members. The
standard deviation (S.D) of the set S can be
found by the square root of variance S .D  V
which gives us the spread out of data from
mean. We add up the mean M of set S with the
standard deviation S.D to set that value as the
threshold level. The disperse node(s) has (have)
a mean average distance greater than the
threshold level which is shown in Fig.2. For
verification of our hypothesis in this subsection,
we take an example- let a network contains CHs
having co-ordinates {(0,0), (0,5), (0,10), (5,0),
(5,5), (5,10), (10,0), (10, 5), (10,10), (20,10)}.
However, it would be nice ideas to set up
different threshold levels aiming to get different
numbers of disperse CH(s). We leave this issue
as a future research topic for interested readers.
In this paper, we have set up the example case
with a single disperse CH.
3.
For each CH
4.
Find the distance from (n-1) CHs and
store the values inside a set.
5. End Loop
6. Start Loop (1:n)
7.
For each set find the mean value and
store value inside a set S.
8. End Loop
9. M Find the mean value from the set
10. S.D Find standard deviation from the
mean
11. Set threshold level equal to (M+S.D).
12. Find out the CHs that have a mean value
greater then the threshold level
13. Return CHs
5 Relay Station Positioning
Before proceeding the analysis a consideration
of the presence of only the disperse CHs and the
BS will help us to figure out the optimal
positions for relay stations. The conceivable
dispersive nature of the CHs are depicted in the
following figure
(a)
(c)
At first a list of questions is prepared and then
the answers of those questions are figured out.
i)
ii)
iii)
Why do we need relay stations?
How many relay stations are to be
placed?
Where should we place those relay
stations?
(b)
(d)
Fig.3: Conceivable dispersive nature of nodes: (a) and (b) Single sided dispersion (c) double sided
dispersion (d) four sided dispersion
Disperse
node
Position
of furthest
disperse
node
Relay
position
Position 3
Position 2
Position 1
(a)
Disperse
node
Relay
positions
Fig.4: Relay positioning
The absence of any relay station hinders
the alteration of BS position which is determined
to be the center of the minimum enclosing circle
that encloses all the CHs in topology(T1).
Consequently, enhancing network lifetime as a
result of the alteration of BS position becomes
an unfeasible scheme.
The numbers of relay stations to be
placed in the network is left as a designer’s
choice. Before designing a network with relay
stations designers need to consider some factors
such as cost, connectivity of the network,
network coverage, dispersive nature of the CHs
and so on. However, if a discrete relay station is
burdened as being assigned to relay data for
many CHs, its energy might be depleted well in
advance the CHs deplete their energy.
Conversely, if we are not limited by the number
of relay stations the problem turns out to be an
assignment problem (assigning the CHs with the
BS).
The driving idea is to reduce the burden
of the relay stations and we can do that by
placing more than one relay station at a close
distance and divide the number of CHs by the
number of available relay stations to complete
the assignment process. The simulation results in
the following section give a good insight
regarding this matter.
Disperse
node
(b)
Fig.5: Position of relays for two different BTS(a) one relay for 2 BTS (b) Two relays for 2
BTS
The dispersive nature of the CHs also
determines the least number of relay stations
required in this conceived scheme. From the
above figures we conclude that,
For case 1, at least one relay station is required.
For case 2, at least two relay stations are
required.
For case 3, at least four relay stations are
required.
For case 2 and case 3, we need more than one
relay station since disperse nodes are present at
both sides of the BS or sink.
If a single relay station is to be placed
then the best possible position for a relay station
lies on the line connecting the farthest disperse
CH on one side and the BS. The point on the
line will have to be determined by the ratio of
the number of disperse CHs on that side and the
number of available relay stations. As the
number of disperse CHs increases the position
also comes closer to the BS. In positioning the
relay stations a comparison between the
depletion rate of energy of the CHs and the relay
stations is required to maintain the balance since
the depletion of energy of any of the relay
stations will result in a loss of network coverage.
A similar analogy can be obtained for any of the
two or four sides of the BS.
Disperse
node
Relay
positions
(a)
Disperse
node
Relay
positions
Disperse
node
(b)
Fig.6: Position of relays for two different BTS(a) Two relay for 2 BTS on one side (b) Four
relays for 2 BTS on both side
6 Simulation Results
First graph in this section gives us the insight
about the optimal position for a relay station
while disperse CHs are considered to be at one
side of the BS. Three positions are considered
for evaluation to elucidate the outcome of
positioning relay stations at different points. At
first a straight line is considered as the joining
line between the farthest disperse CH’s position
and altered BS position. While all the three
points lie on the line, the first point (position 1)
is deliberated to be on thecircumference of the
circle, the third point (position3) is deliberated
as the midpoint between the farthest disperse CH
and the unaltered BS position and the third point
is chosen as the midpoint of position 1 and
position 3.
In Fig.7(a), the disperse CHs are
considered to be at one side of the BS,I Fig.7(b)
for disperse CHs considered to be present at two
sides of the BS and fig.7(c) considers the
disperse CHs to be present at four sides of the
network. The best result occurs for position 1 in
all three cases considering some discrepancies
observed in those graphs which might have been
caused by the less dispersive nature of the
network. We conclude that the point on the
circumference of the circle that excludes
disperse CHs is the best position for relay
station. The outcomes of the simulations are in
harmony with the prediction made through
analysis provided in section 4.
Fig.8 demonstrates that network lifetime
is improved when we use relay stations and alter
the BS position rather than sticking to the
position considered as the best one devoid of
relay stations. For the 4-sided 4-relay scheme
the best result is obtained. Since the CHs
positions are randomly generated, the dispersed
CHs may be found at any side of the BS. If we
use 1 sided single relay or 2 sided double relay,
some disperse CHs may remain unassigned
causing the downfall of the network lifetime.
In Fig.9(a), for various numbers of
disperse nodes the relay station’s proximity to
BS is determined from the relay station to
(a)
(b)
(c)
Fig.7: Lifetime vs. percentage of disperse node in terms of total number of nodes-(a) distribution of
disperse node according to Fig.3(a) or 3(b).(b) distribution of disperse node according to Fig.3(c).(c)
distribution of disperse node according to Fig.3(d). Relay positions 1, 2 and 3are shown in Fig.5.
disperse nodes ratio. First a single and then two
relay stations are considered. As expected from
our analysis, lifetime is improved when number
of available relay stations has been increased.
Since more than one relay station is available,
pressure of relaying data is relaxed. Thus the
lifetime is improved in case of two relay
stations.
Fig. 8: Lifetime vs. Number of cluster head graph comparing among four different relay positioning
scheme
(a)
(b)
Fig.9: Lifetime vs. Percentage of disperse node graph for two BTS scheme-(a) relays at one side of the
BTSs (b) relays at both sides of the BTSs
In Fig.9(b), the disperse nodes are considered to
be present at both sides of the BS. The
dispersive nature of the disperse nodes make it
necessary to use at least two relay stations since
they are present at both sides of the BS. For two
relay stations to be placed at both sides of the
BS, the analysis provided above remains valid
since the problem can be rationalized as disperse
nodes present at one side and a single relay
station is available. Similarly for 2 sides 4 relays
the problem can be simplified as disperse nodes
present at one side of the BSs and two relay
stations are available. A better lifetime is
obtained as the number of available relay station
increases.
7 Conclusion
In an energy constrained wireless sensor
network, network lifetime can be enhanced
through a little deviation from the direction
given in the earlier studies about the placement
of the BS. To enable the feasibility of changing
the BS position, relay stations are thought of as a
viable solution. An improvement in the network
lifetime is achieved through the use of relay
stations. Optimal placement of the relay stations
also plays a crucial role in this process. A
comprehensive analysis is provided to give a
good insight on this issue to the readers.
Simulation results complement our claims.
Acknowledgement
The discussion provided in section IV has been
taken from our previous work [10].
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