Multihop/Direct Forwarding for 3D Wireless Sensor

Networks Preety Sharma

Galgotias College of Engineering and Technology

Greater Noida, India

preetysre@gmail.com

Sansar Singh Chauhan Accurate Institute of Management

and Technology Greater Noida, India

sansar@gmail.com

Sandeep Saxena Galgotias College of Engineering and

Technology Greater Noida, India

sandeepsaxena4444@gmail.com

ABSTRACT Wireless Sensor Networks (WSNs) are limited in their energy,

computation and communication capabilities. Energy efficiency

[3] and balancing is one of the primary challenges for Wireless

Sensor Networks since the sensor nodes cannot be easily

recharged once they are deployed. The consumption of energy is

majorly determined by the data forwarding schemes. These

schemes are employed to transmit the sensed information to the

final destination. In this work, we analyze the behavior of

Multihop/Direct Forwarding (MDF) [6] scheme, when applied to

the sensor network deployed in three dimensional fields. The

results of simulation are then compared with some other data

forwarding schemes. Simulation results show that MDF scheme in

3D can balance the energy consumption for all sensor nodes. The

network lifetime is prolonged in case of MDF compared to other

data forwarding techniques when applied in three dimensional

fields.

Keywords

Wireless Sensor Networks, energy consumption, network lifetime,

MDF

1. INTRODUCTION Advancement in the field of Wireless Communication has lead to

the development of Wireless Sensor Networks (WSN) [1]. These

networks consist of small devices known as nodes. Each sensor

node has a processor, radio, sensor and built-in battery. A node

senses the region over which it is deployed and transmits the

sensed data to the Base Stations. The stations may be single or

multiple depending upon the nature of WSN applications. The

major contribution of the Wireless Sensor Networks lies in

commercial as well as industrial areas. Some applications of WSN

are habitat monitoring [2], monitoring of an active volcano [13],

structural health monitoring, forest fire and surveillance system

[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

sensed information to the Base Station. The major issue with

WSN is the dependency of each node on the battery for its

activities, which is severely limited. In most cases, recharge as

well as replacement of the battery is not recommended. Therefore,

the usage of limited battery must be estimated accordingly [14].

WSN employs various data forwarding schemes. These schemes

are required to deliver the sensed data to the destination. They

play an important role in increasing the lifespan of a network [3].

Moreover, they reduce the energy consumption of the node and

network as a whole. There are a number of data forwarding

techniques, like Closest Forwarding (CF), Direct Forwarding

(DF), Multihop Forwarding (MF) and Multihop/Direct

Forwarding (MDF).

In this work, we focus on the Multihop/Direct Forwarding

technique [6] to be implemented for 3D Wireless Sensor

Networks. These sensors are assumed to be deployed in three

dimensional fields. We have used an approach wherein we need to

find the optimum transmission schedule of the nodes. This can be

determined by dividing the packet flow of each node so that the

battery lifespan can be increased. The results of MDF are then

compared with different forwarding schemes on the basis of

network lifetime and energy consumption. We have considered a

3D Network Model with uniformly distributed nodes such that the

projection of the 3D Network resembles a conical view. The Base

Station is assumed to be present at the apex of the cone. This 3D

Network Model has its applications in the field of surveillance.

Our contributions in this study are twofold. First, we have derived

equations for packet flow division rules for 3D Wireless Sensor

Networks. Second, simulations for the evaluation of MDF scheme

in 3D are carried out.

The rest of the paper is organized as follows: In section 2,

foundation and problem composition are presented. We then

present the various forwarding schemes in section 3. In section 4,

MDF technique in case of 3D Wireless Sensor Networks is

discussed and section 5 presents and analyzes the simulation

results. Finally, we conclude our work in Section 6.

2. FOUNDATION AND PROBLEM

COMPOSITION We consider a 3D Wireless Sensor Network in which sensor

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

divided into logical nodes and each logical node is at 1 unit

distance from its consecutive logical node. The number of nodes

in any logical node is proportional to the difference in the surface

areas of the subsequent logical nodes [4][12]. Therefore, the

number of nodes at any logical node l having radius rl where l is

the distance of the node from the Base Station is given by:

(1)

2.1 Assumptions Any kind of transmission loss is not considered in the

analyses.

Receiving node does not consume extra energy in

packet reception [7].

Each node has the capability to adjust its transmission

range.

The node can send the packet directly to the Base

Station if required [10].

The distance between each logical node is assumed to

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

Base Station. The logical nodes are indexed in the

increasing order from their distance to the Base Station.

The logical node closest to the sink has the least index

with the index „0‟ assigned to the Base Station.

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.

The energy spent in sending one packet from logical

node u to logical node v is given by

E = k0 + (u-v) w (2)

where k0 is the energy constant. It includes the total

energy spent by the node in reception or being idle and

w is the path loss exponent and its value is assumed to

be 2 in this work[7][10].

The total energy consumption of node u is given by:

ETC[u] = + ] (3)

t is the optimal transmission range[8] where

t )1/w) (4)

2.3 Problem Formulation To evaluate the performance of the MDF scheme in a 3-

Dimensional conical network. The network consists of nodes

deployed in such a way that the base station is present at the apex

of the network. In order to evaluate its performance under the

MDF scheme, we have to find out the packet flow rate, Pu,v. where

u, v {0, 1… N} such that the energy spent by the whole network

is minimized and the lifespan of the network is maximized

[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. SOME DATA FORWARDING

TECHNIQUES AND THEIR ENERGY

CONSUMPTION There are numerous data forwarding techniques used in WSN

depending upon the requirement. The amount of energy consumed

to forward the data is different for different techniques. We will

discuss the various techniques and present the energy

consumption of the nodes for the 3D network.

3.1 Closest Forwarding Technique: This is the

forwarding technique in which each sensor node forwards its

packets to its closest node towards the Base Station as shown in

figure1. In this scheme, the energy consumption of each node is

different. The node closest to the Base Station handles the

maximum amount of packets [11]. Therefore, it consumes

maximum amount of energy [9]. For any logical node u, lying at a

distance u from the Base Station, the energy consumption is given

by: ECF[u] = (3rN

2 + 3 r(N-1)2 +---+ 3ru

2)(k0 +1w) (5)

3.2 Direct Forwarding Technique: This is the forwarding technique in which each sensor node

forwards its packets directly to the Base Station. Therefore, Pu, v=0

except when v=0. The energy consumption of the nodes in the DF

technique is also unbalanced. The energy consumption of the

node increases with increase in distance from the Base Station.

The node farthest from the Base Station consumes the maximum

amount of energy. Therefore, for any node u, the energy

consumption is given by:

EDF[u] = 3ru2(k0 + uw) (6)

where ru is the radius of the logical node u.

N

N-1

N-2

1

2

3

Base Station

Figure 1: Closest Forwarding Technique

.

3.3 Multihop Forwarding Technique: This is the forwarding technique in which each node forwards its

data packets to the node lying at the optimum hop distance, t

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

distance t. Therefore, Pu, v=0 except when u-v= t or when u<t and

v=0

EMF[u] = (3rN2 + 3r(N-t)

2 + …+3ru2)(k0+min(t,u)w) (7)

where ru is the radius of the logical node u.

We calculated the energy consumption of different logical nodes

as per the above mentioned schemes (CF, DF and MF). The

results are shown in Figure 4. We have observed that the node

energy consumption of the DF scheme increases with increase in

the distance from the Base Station. The CF scheme exhibits a

reverse trend. In the case of CF, node energy consumption

increases with decrease in the distance from the base station. The

MF scheme leads to much more balanced energy consumption as

compared to CF and DF scheme.

Figure 4: Comparison of node energy consumption for CF, DF

and MF techniques (N=50, k0=100)

4. MULTIHOP/DIRECT FORWARDING

(MDF) FOR 3D WSN In the Multihop/Direct Forwarding Scheme each logical node x

divides its data packets into two components. The first component

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

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,

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

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.

The logical nodes in the whole network are divided into t

subgroups. Each logical node except the last node in a single

subgroup is separated from its consecutive logical node by a

distance t. The last node may be at a distance lesser than t units to

the Base Station. We further assume that each subgroup has its

own Base Station. Hence, the number of Base Stations is equal to

the number of subgroups i.e. t. Each subgroup sends its packets

separately to the Base Station. We will analyze the behavior of

only one of these subgroups as shown in figure 5 since each of

them is essentially the same.

5 10 15 20 25 30 35 40 45 500

1

2

3

4

5

6

7

8x 10

5

Node index,uE

nerg

y C

onsum

ption,

E[u

]

CF

DF

MF

N

N-t

t+1

1

Base Station

N

N-1

N-2

1

2

3

Base Station

Figure 2: Direct Forwarding Technique

Figure 3: Multihop Forwarding Technique

.

We initiate the study of 3D WSN, by analyzing the behavior of

one of the subgroups. In a subgroup, the total number of logical

nodes that are sending data to the Base Station is denoted by z

where z = (8)

where N is the total number of logical nodes and t is the optimum

hop distance. If we analyze any logical node say x where 1<x<z,

then the packet flow of node xt can be represented as:

P(x+1) t, xt + = Pxt, (x-1) t + Pxt ,0 (9)

where xt = 3(rxt) 2

The energy spent in sending a packet from node (x+1) t to node xt

is given by:

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

the network, we need to make sure that the energy spent by logical

nodes (x+1) t and xt must be equal. Hence:

=

(11)

We can define

Gx = (12a)

Hx = (12b)

where x= 2, 3 4… z

Therefore, eq (12a) and (12b) can be rewritten as:

Gx+1 + Hx+1 = Gx + Hx =…..=G3 + H3 = G2 + H2 (13)

Similarly, eq (11) can also be rewritten as:

Gx = Gx-1 + P(x-1) t, 0 (14)

Putting x=1 in eq (9), we get:

P2t, t + = Pt ,0 (15)

Since the energy consumption of nodes 2x and x must be same.

Therefore:

P2t,t * (k0 + tw) + P2t,0* (k0 + 2tw) = Pt,0* (k0 + tw)

4

P2t, t + P2t, 0 * (k0 + 2tw) = 4Pt,0 (16)

(k0 + tw )

Therefore, eq (15) can be rewritten as:

G2 = (17)

Similarly, combining eq (15) and eq (16), we get:

H2 = (18)

Hence:

G2 + H2 = (19)

From eq (13), we get:

Hx = Pt, 0 – Gx (20)

We can calculate the value of Pxt, 0 from eq (12b):

Pxt, 0 = [x2* Hx ] (21)

where x=2, 3…z.

Putting the value of x=2 in eq (21), we get:

P2t,0 = [3Pt,0 + ] (21a)

Similarly, substituting the values for x=3, 4…z, we get eq (21) in

the form:

Pxt, 0 = mxPt, 0 + nx (22)

The boundary condition may be obtained through traffic

generation of all nodes

= = (23)

i.e

=Pt, 0 = (24)

Therefore:

Pt, 0 = –

(25)

and from eq (22) and eq (25)

Pxt,(x-1)t = x2 Pt,0 – Pxt,0* (26)

In order to apply MDF scheme, a node u needs to know its index

i.e. its distance from the base station. Therefore, the value of x in a

subgroup can be calculated as: x = (27)

where is the ceiling function returning the smallest integer that

is not smaller than n.

In order to calculate the energy consumption of any logical node

say u, we are required to know the index of that node. The index

of node u can be greater than or less than the optimum forwarding

distance t, which results in two cases:

Case A: When u>t,

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)

respectively.

Case B: when u<t,

ETC [u] = Pt, 0(k0 + uw) (29)

where Pt,o is given by eq(25) .

zt

(z-1)t

t

2t

(z-2)t

Base Station

Figure 5: Representation of a subgroup in a 3D network

implementing MDF scheme

5. RESULT ANALYSIS This section provides some numerical and simulation results on

the MDF scheme. The MDF scheme in 3D has been evaluated and

compared with other techniques by using MATLAB. We have

used the following model for simulation:

We have assumed a 3D network. The nodes are deployed in a

conical projection. All the nodes lying at the same distance from

the Base Station are grouped into a single logical node. N is the

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.

The distance between any two consecutive logical nodes is 1 unit.

We have compared the results of MDF scheme with other

schemes such as MF, DF and CF in terms of energy consumption

and network lifetime.

Figure 6: Comparison of node energy consumption for the DF,

the MF, and the MDF schemes (N = 50, k0 = 100).

Figure 6 shows the energy consumption of logical nodes under

MF, DF and MDF schemes. We have shown the results in terms

of Normalized Energy Consumption. Each normalized value of

energy consumption of a logical node is actually the ratio of the

fractional consumption of total energy to the minimum value of

fractional energy consumption along all logical nodes. We have

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.

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

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.

When MDF scheme is implemented in 3D, we have evaluated the

values of energy consumption with different hop distance and

k0=100. We have analyzed the results with different values of N.

In order to show the optimality more clearly in figure 7, we

present normalized energy consumption, which is calculated as

the average energy consumption divided by the minimum value of

energy consumption along all possible t, i.e. E/Emin.. It can be seen

that the energy consumption is higher, at small as well as larger

values of t. The least value of energy consumption is at the

optimum hop distance which is calculated in eq.(4). The results

are shown in Figure 8.

Figure 7: Normalized Energy Consumption of different hop

distance t, when MDF scheme is employed and k0=100

.

Figure 8: Normalized energy consumption of different hop

distance, t (N = 50)

25 30 35 40 45 500

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En

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MF

MDF

5 10 15 20 25 30 35 40 45 500.5

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En

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K0=200

5 10 15 20 25 30 35 40 45 501

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3

3.5

hop distance,t

Norm

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nerg

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En

N=50

N=100

N=200

Figure 9 shows the network lifetime for MF, CF and MDF

forwarding techniques. It can be seen that the network lifetime of

MDF scheme is better as compared to other techniques. The

lifetime of the CF technique is significantly shorter than all other

schemes. This is because of the imbalance energy consumption of

nodes in the network. We have defined network lifetime, in Figure

9, as the time when the first node in the network runs out of

battery energy.

Figure 9: Network Lifetime for MF, MDF and CF schemes

6. CONCLUSION In this paper, we presented the MDF technique in case of 3D

WSN and presented the network lifetime and energy consumption

of the nodes. We have identified that the MDF scheme performs

close to some very efficient but complex techniques in terms of

energy consumption. The network lifetime of MDF scheme is far

better as compared other schemes when evaluated in 3D. Thus, it

can be said that MDF scheme shows consistent performance even

in case of 3D.

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