published in ACM CUBE 2012 pune

1. Multihop/Direct Forwarding for 3D Wireless Sensor
Networks
Preety Sharma Sansar Singh Chauhan Sandeep Saxena
Galgotias College of Engineering Accurate Institute of Management Galgotias College of Engineering and
and Technology and Technology Technology
Greater Noida, India Greater Noida, India Greater Noida, India
preetysre@gmail.com sansar@gmail.com sandeepsaxena4444@gmail.com
ABSTRACT well as replacement of the battery is not recommended. Therefore,
Wireless Sensor Networks (WSNs) are limited in their energy, the usage of limited battery must be estimated accordingly [14].
computation and communication capabilities. Energy efficiency WSN employs various data forwarding schemes. These schemes
[3] and balancing is one of the primary challenges for Wireless are required to deliver the sensed data to the destination. They
Sensor Networks since the sensor nodes cannot be easily play an important role in increasing the lifespan of a network [3].
recharged once they are deployed. The consumption of energy is Moreover, they reduce the energy consumption of the node and
majorly determined by the data forwarding schemes. These network as a whole. There are a number of data forwarding
schemes are employed to transmit the sensed information to the techniques, like Closest Forwarding (CF), Direct Forwarding
final destination. In this work, we analyze the behavior of (DF), Multihop Forwarding (MF) and Multihop/Direct
Multihop/Direct Forwarding (MDF) [6] scheme, when applied to Forwarding (MDF).
the sensor network deployed in three dimensional fields. The
results of simulation are then compared with some other data In this work, we focus on the Multihop/Direct Forwarding
forwarding schemes. Simulation results show that MDF scheme in technique [6] to be implemented for 3D Wireless Sensor
3D can balance the energy consumption for all sensor nodes. The Networks. These sensors are assumed to be deployed in three
network lifetime is prolonged in case of MDF compared to other dimensional fields. We have used an approach wherein we need to
data forwarding techniques when applied in three dimensional find the optimum transmission schedule of the nodes. This can be
fields. determined by dividing the packet flow of each node so that the
battery lifespan can be increased. The results of MDF are then
Keywords compared with different forwarding schemes on the basis of
Wireless Sensor Networks, energy consumption, network lifetime, network lifetime and energy consumption. We have considered a
MDF 3D Network Model with uniformly distributed nodes such that the
projection of the 3D Network resembles a conical view. The Base
1. INTRODUCTION Station is assumed to be present at the apex of the cone. This 3D
Advancement in the field of Wireless Communication has lead to Network Model has its applications in the field of surveillance.
the development of Wireless Sensor Networks (WSN) [1]. These Our contributions in this study are twofold. First, we have derived
networks consist of small devices known as nodes. Each sensor equations for packet flow division rules for 3D Wireless Sensor
node has a processor, radio, sensor and built-in battery. A node Networks. Second, simulations for the evaluation of MDF scheme
senses the region over which it is deployed and transmits the in 3D are carried out.
sensed data to the Base Stations. The stations may be single or The rest of the paper is organized as follows: In section 2,
multiple depending upon the nature of WSN applications. The foundation and problem composition are presented. We then
major contribution of the Wireless Sensor Networks lies in present the various forwarding schemes in section 3. In section 4,
commercial as well as industrial areas. Some applications of WSN MDF technique in case of 3D Wireless Sensor Networks is
are habitat monitoring [2], monitoring of an active volcano [13], discussed and section 5 presents and analyzes the simulation
structural health monitoring, forest fire and surveillance system results. Finally, we conclude our work in Section 6.
[9] etc. The success of any network is determined by how
efficiently it delivers data to the destination. Similarly, success of
WSN is determined by how efficiently the nodes deliver the 2. FOUNDATION AND PROBLEM
sensed information to the Base Station. The major issue with COMPOSITION
WSN is the dependency of each node on the battery for its We consider a 3D Wireless Sensor Network in which sensor
activities, which is severely limited. In most cases, recharge as nodes are uniformly distributed. The projection of the nodes is
such that they form a conical appearance. The Base Station lies at
the apex of the cone. The data generation rate of each node is one
packet per unit time. The network has been divided into several
logical nodes. The nodes lying at a distance i, from the Base
Station constitutes the logical node i. This logical node consists of
all the nodes lying at or inside its circumference.
The 3D representation of WSN can be explained with the help of
figure 1. In case of 3D WSN, we assume that the whole network is

2. divided into logical nodes and each logical node is at 1 unit 3. SOME DATA FORWARDING
distance from its consecutive logical node. The number of nodes
in any logical node is proportional to the difference in the surface TECHNIQUES AND THEIR ENERGY
areas of the subsequent logical nodes [4][12]. Therefore, the CONSUMPTION
number of nodes at any logical node l having radius rl where l is There are numerous data forwarding techniques used in WSN
the distance of the node from the Base Station is given by: depending upon the requirement. The amount of energy consumed
to forward the data is different for different techniques. We will
(1)
discuss the various techniques and present the energy
consumption of the nodes for the 3D network.
2.1 Assumptions
 Any kind of transmission loss is not considered in the 3.1 Closest Forwarding Technique: This is the
analyses. forwarding technique in which each sensor node forwards its
 Receiving node does not consume extra energy in packets to its closest node towards the Base Station as shown in
packet reception [7]. figure1. In this scheme, the energy consumption of each node is
 Each node has the capability to adjust its transmission different. The node closest to the Base Station handles the
range. maximum amount of packets [11]. Therefore, it consumes
 The node can send the packet directly to the Base maximum amount of energy [9]. For any logical node u, lying at a
Station if required [10]. distance u from the Base Station, the energy consumption is given
by:
 The distance between each logical node is assumed to ECF[u] = (3rN2 + 3 r(N-1)2 +---+ 3ru2)(k0 +1w) (5)
be 1 unit.
2.2 Notations
 Nodes that are „x‟ units away from the Base Station are
grouped into single logical node „x‟.
 N is the total number of logical nodes, excluding the N
Base Station. The logical nodes are indexed in the
increasing order from their distance to the Base Station. N-1
The logical node closest to the sink has the least index
with the index „0‟ assigned to the Base Station. N-2
 r is the radius of the logical node farthest from the Base
Station .i.e. lying at a distance N from the base station.
 Pu,v. is the rate of packet flow from logical node u to
logical node v. 3
 The energy spent in sending one packet from logical
node u to logical node v is given by 2
E = k0 + (u-v) w (2)
where k0 is the energy constant. It includes the total 1
energy spent by the node in reception or being idle and
w is the path loss exponent and its value is assumed to Base Station
be 2 in this work[7][10].
 The total energy consumption of node u is given by: Figure 1: Closest Forwarding Technique
ETC[u] = + ] (3)
 t is the optimal transmission range[8] where
t )1/w) (4)
3.2 Direct Forwarding Technique:
This is the forwarding technique in which each sensor node
2.3 Problem Formulation forwards its packets directly to the Base Station. Therefore, Pu, v=0
To evaluate the performance of the MDF scheme in a 3- except when v=0. The energy consumption of the nodes in the DF
Dimensional conical network. The network consists of nodes technique is also unbalanced. The energy consumption of the
deployed in such a way that the base station is present at the apex node increases with increase in distance from the Base Station.
The node farthest from the Base Station consumes the maximum
of the network. In order to evaluate its performance under the
amount of energy. Therefore, for any node u, the energy
MDF scheme, we have to find out the packet flow rate, Pu,v. where consumption is given by:
u, v {0, 1… N} such that the energy spent by the whole network EDF[u] = 3ru2(k0 + uw) (6)
is minimized and the lifespan of the network is maximized where ru is the radius of the logical node u.
[10][5]. The lifetime of the network in our work has been defined
as the time when first node of the network runs out of energy.

3. MF scheme leads to much more balanced energy consumption as
compared to CF and DF scheme.
N 5
x 10
8
CF
N-1 DF
7
MF
N-2
6
Energy Consumption, E[u]
5
3
4
2
3
1
Base Station 2
Figure 2: Direct Forwarding Technique
. 1
3.3 Multihop Forwarding Technique:
This is the forwarding technique in which each node forwards its 0
5 10 15 20 25 30 35 40 45 50
data packets to the node lying at the optimum hop distance, t Node index,u
towards the Base Station as shown in figure 3.The logical node N
is forwarding its packets to the node (N-t), which is at hop
Figure 4: Comparison of node energy consumption for CF, DF
distance t. Therefore, Pu, v=0 except when u-v= t or when u<t and
and MF techniques (N=50, k0=100)
v=0
EMF[u] = (3rN2 + 3r(N-t)2 + …+3ru2)(k0+min(t,u)w) (7) 4. MULTIHOP/DIRECT FORWARDING
where ru is the radius of the logical node u. (MDF) FOR 3D WSN
In the Multihop/Direct Forwarding Scheme each logical node x
divides its data packets into two components. The first component
N is sent to the logical node which is t distance away from x,
denoted by Px, (x-t). The second component is sent directly to the
Base Station denoted by Px,0 . If the logical node lies at a distance
N-t which is less than the optimal transmission range t i.e. x ≤ t then
all the packets are sent directly to the Base Station. The number of
packets generated by each logical node is equal to the number of
nodes present. The number of nodes in a logical node is 3rl2
where rl is the radius of the logical node (as calculated in eq(1)).
Since the number of nodes in each logical node is different,
t+1 therefore each logical node is heterogeneous in terms of energy
reserve as well as packet generation. The energy reserve and the
number of packets are proportional to the number of nodes at that
1 logical node. Hence, all the nodes which are at the same distance
from the Base Station are grouped into a single logical node
having energy reserve and as the total number of packets
generated.
Base Station
The logical nodes in the whole network are divided into t
Figure 3: Multihop Forwarding Technique subgroups. Each logical node except the last node in a single
subgroup is separated from its consecutive logical node by a
We calculated the energy consumption of different logical nodes distance t. The last node may be at a distance lesser than t units to
as per the above mentioned schemes (CF, DF and MF). The the Base Station. We further assume that each subgroup has its
results are shown in Figure 4. We have observed that the node own Base Station. Hence, the number of Base Stations is equal to
energy consumption of the DF scheme increases with increase in the number of subgroups i.e. t. Each subgroup sends its packets
the distance from the Base Station. The CF scheme exhibits a separately to the Base Station. We will analyze the behavior of
reverse trend. In the case of CF, node energy consumption only one of these subgroups as shown in figure 5 since each of
increases with decrease in the distance from the base station. The them is essentially the same.

4. Since the energy consumption of nodes 2x and x must be same.
Therefore:
zt
P2t,t * (k0 + tw) + P2t,0* (k0 + 2tw) = Pt,0* (k0 + tw)
4
P2t, t + P2t, 0 * (k0 + 2tw) = 4Pt,0 (16)
(z-1)t (k0 + tw )
Therefore, eq (15) can be rewritten as:
G2 = (17)
(z-2)t Similarly, combining eq (15) and eq (16), we get:
H2 = (18)
2t Hence:
G2 + H2 = (19)
t From eq (13), we get:
Hx = Pt, 0 – Gx (20)
Base Station We can calculate the value of Pxt, 0 from eq (12b):
Pxt, 0 = [x2* Hx ] (21)
where x=2, 3…z.
Figure 5: Representation of a subgroup in a 3D network
. Putting the value of x=2 in eq (21), we get:
implementing MDF scheme
P2t,0 = [3Pt,0 + ] (21a)
We initiate the study of 3D WSN, by analyzing the behavior of
one of the subgroups. In a subgroup, the total number of logical Similarly, substituting the values for x=3, 4…z, we get eq (21) in
nodes that are sending data to the Base Station is denoted by z the form:
where z = (8) Pxt, 0 = mxPt, 0 + nx (22)
where N is the total number of logical nodes and t is the optimum
The boundary condition may be obtained through traffic
hop distance. If we analyze any logical node say x where 1<x<z, generation of all nodes
then the packet flow of node xt can be represented as:
= = (23)
P(x+1) t, xt + = Pxt, (x-1) t + Pxt ,0 (9)
where xt = 3(rxt) 2 i.e
The energy spent in sending a packet from node (x+1) t to node xt =Pt, 0 = (24)
is given by: Therefore:
P(x+1) t, xt *(k0 + tw) + P(x+1) t, 0 *(k0 +(x+1) tw) (10) –
Therefore, in order to balance the consumption of the energy in Pt, 0 = (25)
the network, we need to make sure that the energy spent by logical and from eq (22) and eq (25)
nodes (x+1) t and xt must be equal. Hence:
Pxt,(x-1)t = x2 Pt,0 – Pxt,0* (26)
=
In order to apply MDF scheme, a node u needs to know its index
(11) i.e. its distance from the base station. Therefore, the value of x in a
We can define subgroup can be calculated as: x = (27)
where is the ceiling function returning the smallest integer that
Gx = (12a)
is not smaller than n.
In order to calculate the energy consumption of any logical node
Hx = (12b) say u, we are required to know the index of that node. The index
where x= 2, 3 4… z of node u can be greater than or less than the optimum forwarding
distance t, which results in two cases:
Therefore, eq (12a) and (12b) can be rewritten as: Case A: When u>t,
Gx+1 + Hx+1 = Gx + Hx =…..=G3 + H3 = G2 + H2 (13) ETC [u] = Pxt, 0 (k0 + uw) + Pxt,(x-1)t(k0 + tw ) (28)
where Pxt,0 , Pxt,(x-1)t and x are given by eq (22) ,(26) and (27)
Similarly, eq (11) can also be rewritten as: respectively.
Gx = Gx-1 + P(x-1) t, 0 (14) Case B: when u<t,
ETC [u] = Pt, 0(k0 + uw) (29)
where Pt,o is given by eq(25) .
Putting x=1 in eq (9), we get:
P2t, t + = Pt ,0 (15)

5. 5. RESULT ANALYSIS In order to show the optimality more clearly in figure 7, we
This section provides some numerical and simulation results on present normalized energy consumption, which is calculated as
the MDF scheme. The MDF scheme in 3D has been evaluated and the average energy consumption divided by the minimum value of
compared with other techniques by using MATLAB. We have energy consumption along all possible t, i.e. E/Emin.. It can be seen
used the following model for simulation: that the energy consumption is higher, at small as well as larger
We have assumed a 3D network. The nodes are deployed in a values of t. The least value of energy consumption is at the
conical projection. All the nodes lying at the same distance from optimum hop distance which is calculated in eq.(4). The results
the Base Station are grouped into a single logical node. N is the are shown in Figure 8.
total number of logical nodes. Each logical node contains 3*rad^2
number of nodes (where rad is the radius of the logical node).
These nodes are assumed to generate 1 data packet per unit time.
3.5
The distance between any two consecutive logical nodes is 1 unit.
We have compared the results of MDF scheme with other
K0=50
schemes such as MF, DF and CF in terms of energy consumption K0=100
3
and network lifetime. K0=200
Normalized energy Consumption , En
25
2.5
22.5
DF
20 MF
2
MDF
Normalized Energy Consumption, En
17.5
1.5
15
12.5
1
10
7.5 0.5
5 10 15 20 25 30 35 40 45 50
hop distance, t
5
2.5 Figure 7: Normalized Energy Consumption of different hop
distance t, when MDF scheme is employed and k0=100
0
25 30 35 40 45 50
Node Index,u
.
Figure 6: Comparison of node energy consumption for the DF,
3.5
the MF, and the MDF schemes (N = 50, k0 = 100).
N=50
Figure 6 shows the energy consumption of logical nodes under N=100
N=200
MF, DF and MDF schemes. We have shown the results in terms
3
of Normalized Energy Consumption. Each normalized value of
energy consumption of a logical node is actually the ratio of the
Normalized Energy Consumption, En
fractional consumption of total energy to the minimum value of
fractional energy consumption along all logical nodes. We have 2.5
observed that the fractional consumption of total energy of each
logical node is equivalent in case of MDF whereas in case of MF,
it decreases with increase in node index. The DF scheme in case
of 3D model follows the same trend as in one-dimensional model. 2
The fractional consumption of total energy decreases as the
distance from Base Station increases.
In figure 7, we evaluate the values of energy consumption and 1.5
present the Normalized Energy Consumption of the MDF scheme
as a function of t for different values of k0. The number of logical
nodes is fixed at N= 50. It is observed that the value of optimum
hop distance t, increases with increase in k0. 1
5 10 15 20 25 30 35 40 45 50
hop distance,t
When MDF scheme is implemented in 3D, we have evaluated the
values of energy consumption with different hop distance and Figure 8: Normalized energy consumption of different hop
k0=100. We have analyzed the results with different values of N. distance, t (N = 50)

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