Determination of Optimal Number of Relays Using a New Energy Model for WSN

Wireless Sensor Networks are proving themselves as a boon to the surroundings and its deployment in a prominent area is to be considered for minimum energy consumption. In this paper, we have considered deployment of a sensor grid network for 36 and 100 number of sensor nodes. Diagonally opposite nodes are considered to be source and destination. Using a modified energy model, the energy consumption for direct path and that with different number of relays are calculated. The maximum distance up to which direct transmission is possible and the number of required relays for higher transmission distances are then found out.


INTRODUCTION
A sensor network is an infrastructure comprised of sensing, computational and communication elements that give an administrator the ability to instrument observe and react to the events and phenomenon in a specified environment. There are four basic components in a sensor network like an assembly of distributed or localized sensors, an interconnected network, a central point of information clustering ,a set of communication resources at the central point to handle data correlation and event trending etc. In Wireless sensor network (WSN) the sensor nodes are used & they are also called as motes (very small in size) which are used to transmit information from once place to another place like from one node to an another node [1]. Sensors are interconnected via a series of multi-hop short-distance low power wireless link. Power consumption is a prominent issue to be considered as a design constraint. Here we are taking into consideration the fact such as Energy consumption in a sensor network up to a certain distance [2].The lifetime of a sensor node is very less so it is efficient to transmit the information from one sensor node to an another node [3][4][5][6].The sensor nodes also use sleep & idle modes for the sake of an efficient battery.
Sensor nodes have many applications & thus so are used in many areas like in military, Intelligent home, Atmospheric conditions detection (e.g. temperature, humidity, pressure, sound, light) in inventory control, and in disaster management etc. Placement of the sensor nodes in these applications is random in nature or these can be placed manually. For example in military, a large number of sensors are dropped from a helicopter to the required place from where they want to fetch information.
A sensor node contains a sensing unit, processing unit, transceiver unit, & power unit [7]. Sensor nodes do tasks like processing, radio transmission-reception, sensing and actuating. In this paper we are discussing the power consumption and the maximum distance of transmission using relay nodes in a square area grid network of 6*6 and 10*10 dimensions. The structural view of sensor network is shown in Figure 1.

ENERGY MODELING FOR WSN
As in wireless sensor network, one sensor node can transmit the information via two ways: One by direct link & second by node to node delivery .In second case the number of relay nodes can be used which results into reduce in the power consumption required for the transmission to transmit a data from the source node to the destination node these relay nodes will act as a router which receive the data, amplify the data signal and forward it to next neighbor. Receiving, amplifying, and forwarding of the data can be expressed by the following models [8,9,10,11]. Now, transmitted power can be expressed as: Received power can be expressed as: where: Etx(k ,d ): Power consumption to transmit K bits of data to distance d Erx(K ): Power consumption to receive K bits of data Erxelec ∶ Power consumption in the sensor node receiver circuit to process 1 bit Etxelec : Power consumption in the sensor node transmitter circuit to process 1 bit

PROBLEM FORMULATION
Here, for 6x6 and 10x10 networks, it is assumed that:  (1) and (2) & taken into consideration the source node and destination node as the two farthest nodes in a grid network receiving data along the diagonal path [12].

Analysis of 6x6 Area Grid WSN Network
Here, node 1 is the source node & node 36 is the destination node as shown in Figure 2. The transmission from node 1 to node 2 along a diagonal path can be done by using several cases as discussed below: Case 1: Direct path from node 1 to node 36 without using any relay, the distance calculated from node 1 to node 36 is √2 ddimension: In general, Etot (6x6) = (Transmitted power) + (Amplified Power )+ (Received Power) Thus we get, Etot (6x6) =50,000+200 ddimension 4 (3) Figure 2: wireless sensor nodes in 6x6 deployments Case2: By using relay nodes:  Using one relay : Either Node 8 or Node 29 is taken as relay. Now the data is transmitted from Node 1 to Node 8 & then from Node 8 to Node 36 & similarly for node 29. So the total power consumption after applying equations (1) and (2) (1) and (2) is: Etot6x6=31.04 ddimension 4 +100,000 Case 3:  Using two relays : Taking the pair of nodes like Node (8,15), the data gets transmitted from node 1 to node 8 & then to node 15 and finally to node 36. Similar transmission is considered with (8,29) or (22,29). So the total power consumption after applying equations (1) and (2) is: From the above equation (5), we can conclude that relay at mid position consumes lower power.

Analysis of 10x10 area grid WSN network
Here, node 1 and 100 are the source node & destination node respectively, as shown in Figure 3. The transmission of the data from source node to destination node along diagonal path can be done by using several cases as followed: Case 1: Direct transmission from node 1 to node 100 without using any relay Etot(10x10)−direct= 200 ddimension 4 +50,000 (7

Figure3: wireless sensor nodes in 10x10 deployments
Case2:  Using one relay: We have taken either Node 45 or Node 56 as single relay node. This means we transmit data from Node 1 to Node 45 and then Node 45 to Node 100; similarly for node 56 also.
So the total power consumption after applying Equations (1) and (2) Case3:  Using two relays: Considering the pair of nodes like (34, 67), the data gets transmitted from node 1 to node 34 & then to node 67 and finally to node 100.
So the total power consumption after applying equations (1) and (2) is: Etot(10x10) = 7.41 ddimension 4 + 150,000 The data paths for using different number of relay nodes are shown below in Table 1.
The variation of distances with corresponding relay nodes is being shown graphically in Figure 4.

CONCLUSION
In the present work, we have considered a 10x10 wireless sensor network. It is seen that energy consumption is more in direct transmission compared to the same when transmission is done by using relays. We have calculated direct transmission range and optimal number of relays required for larger coverage area.
[3] Apala Ray, "Planning and analysis toll for large scale deployment of wireless sensornetwork", International journal of next generation networks(IJNGN),Vol.