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 2-Dimensional 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 i1

th 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)/(k-1)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 ,

E[Ri]= jP[Ri=j]

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

0

K i

j

Problem 1

Furthermore we have

P[Tk=1]=1

P[Tk=0]=0Thus 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,

E[Ri]= 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)]

0

K i

j

1

0

K i j

l

Problem 1

Analysis for random placement of nodesHere 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 x i=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 as the random variable denoting the energy dissipated by the ith node then we have

E[ ]= e1i +aidn[3n+1-1]/(2n+1(n+1) ) i=1

E[ ]= [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

i

ii

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 LIFETIME

Shelby(equidistant)

Shelby(optimal)

Ashraf Our scheme

58016 secs

110710 secs

142280secs

168620secs

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=(M-1)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 tolerance.

References

1 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.

2 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.

3 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.

4 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.

5 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

6. I. F. Akyildiz, W. Su, Y. Sankarasubhramanium and E.Cayirci, “Wireless Sensor Networks : A Survey”, Computer Networks Journal, Elsevier Science, March 2002, vol. 38,pp. 393-422.

7. I. F.Akylidiz, Dario Pompili, Tommaso Melodia, “Underwater acoustic sensor networks: Research challenges”,Ad-hoc Networks Journal, Elsevier Science,January 2005,vol. 3,pp. 257-279.

8 Jie Wu,Shuhui Yang, “Coverage Issues in Sensor Networks with Adjustable Ranges”, in the proceedings of International Workshop on Mobile and Wireless Networking (MWN 2004),Montreal,Quebec,Canada, 15-18 Aug. 2004(in conjunction with ICPP).

9 C.F.Chiasserini and M.Garetto, “Modeling the performance of Wireless Sensor Networks”, in the proceedings of IEEE INFOCOM-04,Hong Kong, 7-11 March, 2004

10 Ashraf Hossain,T.Radhika,S.Chakrabarti and P.K.Biswas, “An approach to Increase the Lifetime of a Linear Array of Wireless Sensor Nodes”.