WIRELESS SENSOR NETWORKS
G.Balasubramanian
Anand Seetharam
Abhishek Bhattacharyya
Ashraf Hussain
Under the guidance of
Prof. Saswat Chakrabarti
PROBLEM FORMULATION
WSNs being energy constrained systems, one
major problem is to employ the sensor nodes in
such a manner so as to ensure maximum coverage
and connectivity with minimal or optimal number
of nodes and furthermore elongate network
lifetime with maximum energy utilization.
The problem addressed has been tackled for 1-D
linear array and further extended to 2-Dimensions
as stated in the next slides.
PROBLEM STATEMENTS
Problem 1. For a linear array of nodes, we have
devised a system which ensures 100 percent
energy utilization and 100 percent coverage. We
have also derived the optimal number of nodes for
our model so that total energy dissipation is
minimal per data gathering cycle for the entire
network still guaranteeing 100 percent energy
utilization. Furthermore the network lifetime has
also increased as compared to previous studies
mentioned later.
We have also modeled our system for realistic
channels where we have assumed Rayleigh fading
and tried to establish 100 percent energy
utilization.
PROBLEM STATEMENTS
Problem 2. The model developed for a
linear array has been extended to a 2Dimensional array where we consider a
mobile sink which moves linearly in order
to gather data from the proximal nodes in
each of the linear arrays.
LITERATURE SURVEY
Literature survey for previous works in this
context
 [Bha’01] has tried to find out the maximum lifetime of sensor networks but
has assumed that only one node is generating a packet of information while all
the other nodes are involved only in relaying the data and not in generating
packets of their own which is seldom the case.
 [Hae’03] has tried to achieve equal energy dissipation of all the nodes in the
network( considering realistic channels) and has shown how this increases the
network lifetime. But the author has considered only energies involved in
transmitting a packet and has neglected energies involved in receiving a
packet and the idle state energy.
 [She’05] has found the optimal placement of nodes required for minimal
energy dissipation of the network but has overlooked the energy dissipation of
the individual nodes which actually determines the network lifetime. Moreover
with this optimal spacing the radio range required to maintain connectivity
between the nodes becomes extremely large.
LITERATURE SURVEY
 [Xue’06] has considered the case of a 2-D network, but has considered
only energies involved in transmission and reception of signals.
Moreover the author too has tried to maximize the network lifetime by
minimizing the total energy of the network instead of considering the
individual nodes.
 [Gao’06] has considered energies dissipated by the nodes in the
transmitting, receiving and idle states and has tried to minimize the
energy dissipation by the nodes by considering variable radio ranges.
However this is again something which is very difficult to obtain in
practice.
 In [Ashraf ’07], although full energy utilization has been considered,
100 percent coverage and connectivity is not ensured and the sensing
and radio ranges become abnormally large as the number of sensor
nodes increase
PROBLEM 1
•
•
•
•
We have initially modeled the
system for 100 percent energy
utilization.Then for a given
distance D to be covered , we find
the optimal number of nodes for
minimum energy dissipation in a
data gathering cycle.
Then we select the sensing range as
half the internodal distance
considering equispaced nodes.
This gives 100 percent coverage
and if the radio range be twice the
sensing range then connectivity is
also ensured.
We have divided each data
gathering cycle into four states
namely transmission,reception,idle
and sleep in our analysis.
Problem 1
From equal energy dissipation condition it can be established that the idle time
for the ith node can be obtained from that of a reference node i.e.the i1th node
vide the equation
T3i=T3i1+(xT1+yT2)(i-i1) where
x=(et+ ed*dn)/eid and y=er/eid ,et,ed,er,eid being the energy dissipated in the
transmitter electronic circuitry,the energy required for successful transmission
over unit distance,the energy required for successful reception,the idle energy
all being measured per packet per second respectively.
By suitable mathematical analysis, it can be shown that the Kth node serves as the
reference node.
From here, the sleep times for each node can be calculated as the data gathering
cycle lasts for a time Td given by the relation
Td =(k-i+1)*T1+(k-i)*T2+T3i+T4i
where T4i is the sleep time for the ith node.
Problem 1
Optimal spacing of nodes for minimal total energy
dissipation in each data gathering cycle for a
given distance D
dEtotal/dk = 2ketT1+edDnT1*(2k(k-1)-nk2)/(k1)n+1+erT2(2k-1)+eidTidle_min
For equal placement of nodes d=D/(k-1).
Since D is known the above equation is equated to
0 and solved for k by MATLAB simulation
whereby we obtain the optimal number of nodes
distance D.
Problem 1
• Since Berkley mica motes
have a maximum data rate
of 40Kbps, we have
considered transmission at
half the data rate i.e. at 20
kbps and the energies
et,er,eid have been taken in
the ratio 2.5:2:1.
The value of K for a distance
D=6000m. is 141 whence
the sensing range is
21.42m.
The value of K for a distance
D=3000m. is 74 whence
the sensing range assumes
20.55m.
Problem 1
Analysis considering realistic channels for
data gathering network
Let p be the probability that a packet transmitted by a node is received by its nearest
neighbor.Considering Rayleigh Fading Link Model and zero interference network, we
get p=exp(-φσz2/Pod-n) as described in [Hae ’03].
Let Ri & Ti be the random variables denoting the number of packets received and
transmitted by the ith node in a data gathering cycle respectively.
Therefore we have ,
K i
E[Ri]= jP[Ri=j]
j0
Moreover we have ,
P[Ri=x]=P[Ti=x+1]
The number of packets received by the ith node depending on the number of packets
transmitted by the (i+1)th follows a binomial distribution
P[Ri=a|Ti+1=b]=bCapa(1-p)b-a
Problem 1
Furthermore we have
P[Tk=1]=1
P[Tk=0]=0
Thus by recursion we can find out all the probabilities and thus the expectation of
the number of packets can also be found out.
Thus we get,
K  i K  i  j 1
E[Ri]=  
j0 l 0

P[Ri+1=j+l-1]j+l Cjpj(1-p)l
If
is the random variable denoting the energy dissipated by the ith node in
one data gathering cycle, then as before considering a reference node we can
find out the idle times for the different nodes for equal energy dissipation by
equating the expectations of their energies. Thus we have,
T3i =T3i1 +[xT1+yT2][ E(Ri)-E(Ri1)]
Problem 1
Analysis for random placement of nodes
Here we consider random placement of nodes within certain constraints. If x i denotes the
position of the ith node from the sink considering equidistant placement of nodes then
xi=D/k. We assume that each node has an equal probability of being placed at all points
lying within distances ‘d/2’ on either side of xi. If Yi and Zi be the Random Variables
denoting the positions and the inter-nodal of the ith node.
So we get,
Zi=Yi
i=1
Zi=Yi – Yi- 1
2  i
K


Similarly if we take i as the random variable denoting the energy dissipated by the ith
node then we have
E[ i ]= e1i +aidn[3n+1-1]/(2n+1(n+1) )
i=1
E[ i ]= [e1i/2 +aidn/(n+2)] +2[e1i+ ai(2n+1-1)dn/(n+1)] – [e1i(3d2/2 + ai(2n+2-1)dn/(n+2)]


2
i  K
Problem 1
Comparison with
previous papers
MATLAB simulations
show that compared to
both the schemes of
Shelby ’05 the energy
consumption per node
is lesser in our case.
Problem 1
Comparison with previous
papers
MATLAB simulations
show that internodal
distance in Shelby’05 and
Ashraf’07 become too
large as number of nodes
increases and hence the
radio range becomes too
large.
Problem 1
A comparison of network lifetime and energy
consumption demonstrates the efficiency of
our scheme
NETWORK
Shelby Shelby
(equidistant) (optimal)
LIFETIME
Ashraf Our
scheme
58016 110710 142280 168620
secs
secs
secs
secs
PROBLEM 1
Analysis considering finite energy dissipation
during the sleep period
From equal energy dissipation criteria, the idle time
comes out to be
T3i=T3i1+((x-z)T1+(y-z)T2)(i-i1)/(1-z) where z=es/eid es being the energy
per packet per second during the sleep period.
As previously mentioned it can be shown that the Kth node serves as the
reference node even in this case.
Problem 2
Analysis for 2-D arrangement of nodes
Here we consider M rows each being a linear
array of K nodes.We also consider a mobile
sink which moves linearly with a velocity V
to collect data from the terminal node of
each row.
Problem 2
The time required to move
a distance 2rs for the sink
and gather data from the
terminal nodes is given by
T/=KT1+2rs/V and the
total time required to
cover the entire distance is
given by T=(M1)T/.Initially the ith node
sleeps for a time (i-1)T/
and then begins its data
gathering cycle.As a result
data aggregation is
avoided.
The scheme can further be
developed for fault
References
1
2
3
4
5
Zach Shelby,Carlos Pomalaza-Raez,Heikki Karvonen and Jussi Haapola, “Energy
Optimization in Multihop Wireless Embedded and Sensor Networks”, International
Journal of Wireless Information Networks, Springer Netherlands,January 2005,vol
.12,no. 1, pp. 11-21.
Martin Haenggi, “Energy-balancing strategies for Wireless Sensor Networks”, in the
proceedings of the International Symposium on Circuits and Systems (ISCAS 2003),
Bangkok , Thailand,25-28 May, 2003, vol. 4,pp. 45-63.
Q.Gao,K.J.Blow,D.J.Holding,I.W.Marshall and X.H.Peng, “Radio Range Adjustment
for Energy Efficient Wireless Sensor Networks”, Ad-hoc Networks Journal, Elsevier
Science, January 2006, vol. 4,issue 1,pp.75-82.
Qi Xue and Aura Ganz, “On the Lifetime of Large Scale Sensor Networks”,
Computer Communications, Elsevier Science, February 2006,vol. 29, issue 4,pp.
502-510.
Manish Bharadwaj, Timothy Garnett and Anantha P. Chandrakasan, “Upper Bounds
on the Lifetime of Sensor Networks”, in the Proceedings of the International
Conference on Communications (ICC ’01), Helsinki, Finland, June 2001, vol. 3, pp.
785-790.
References
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8
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10
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Ashraf Hossain,T.Radhika,S.Chakrabarti and P.K.Biswas, “An approach to Increase
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