8/12/2019 363-2631323

1/4

ALGORITHMS FOR ENERGY EFFICIENT RECONSTRUCTION OF A PROCESS WITH A MULTIHOP

WIRELESS SENSOR NETWORK

Felipe da Rocha Henriques*, Lisandro Lovisolo, Marcelo Goncalves Rubinstein

*Celso Suckow da Fonseca Federal Center of Technological Education (CEFET/RJ), Petropolis, Brazil

Program of Graduate in Electronic Engineering (PEL), University of State of Rio of Janeiro (UERJ), Brazil

*henriquesfelipe@telpet.com.br, lisandro@uerj.br, rubi@uerj.br

ABSTRACT

In this work, a multihop Wireless Sensor Network (WSN) is

employed to monitor a field, modeled as a process ( ).In order to extend the lifetime of the network, we propose two

algorithms for energy-efficient reconstruction of the monitored

process. The reconstruction of the process is done in sink node, with

samples that it receives from each sensor node. Both algorithms

explore the variation rate of the field to manage the necessity ofcommunication by sensor nodes, aiming at reducing the amount of

transmissions. Furthermore, nodes can sleep between transmissions

to save energy. Simulations are done, and results show a significant

increase in the network lifetime, compared to a WSN without any

energy saving method. The algorithms are evaluated with respect

to the reconstruction error of the field being sensed and network

lifetime increase.

Index Terms Wireless Sensor Networks, Energy, Reconstruc-

tion.

I. INTRODUCTION

Recent advances in microelectronics and wireless communica-

tions made it possible to develop and deploy low cost, low energyconsumption and tiny sensors. These sensors can be used as nodes

in a Wireless Sensor Network (WSN) [1]. A WSN is a special

kind of an ad hoc network and can be applied in areas such as

medicine, with remote monitoring of patients and their biometric

data; military, with monitoring of forces; industrial automation; and

sensing of interest regions, like a forest [2].

In this work, a WSN is considered to sense a field, modeled

as a process that depends on the spatial coordinates and of

sensor nodes, and time . Each sensor node takes samples of the

monitored process and, eventually transmits these measurements

to a sink node. The main objective is to make an energy-efficient

reconstruction of the monitored process. Energy efficiency involves

improving the network autonomy, by increasing its lifetime. In this

work, it is considered that the network lifetime is the time until theenergy of the first node ends [3].

The study of methods that lead to energy saving in a WSN is

an important issue. In [4], a survey of energy saving methods for

WSNs is presented, including a taxonomy of some energy saving

schemes. According to [1], communication (i.e., transmission and

reception) is the task that spends more energy in a WSN. This

means that it maybe advantageous to process data, in order to

decide which measurements have to be transmitted.

In this work, we propose two algorithms for energy conservation

in a multihop WSN. In the proposed algorithms, we intent to reduce

the amount of transmissions of each sensor node, using the variation

rate of the monitored process at the sensor location. The more rapid

is this rate, more transmissions are required by the nodes. Moreover,

nodes can sleep between transmission, in order to save more energy.

The decision whether or not to transmit and sleep is taken locally

by each node individually, that is, in a distributed and decentralized

fashion. The monitored process is reconstructed in the sink node,

using the samples received from sensor nodes.

This work is structured as follows: in Section II, the algorithmsfor energy conservation are presented; Section III presents the

energy model used in this work and simulation aspects; in Section

IV, the results obtained are presented; finally, conclusions are

discussed in Section V.

II. PROPOSED ALGORITHMS FOR ENERGY

CONSERVATION IN A WSN

The presented algorithms run directly in the application layer of

sensor nodes, and aim at saving energy of sensor nodes by using

two strategies: i) To reduce the amount of transmissions, and ii)

to put nodes in a sleeping mode between transmissions. In this

work, we consider a multihop WSN, in which each node is an

information source, when it measures samples from the monitored

process; and also a router (relay), when it has to forward packetsfrom its neighbors.

We assume that a node has an inactivity period , during

which the node does not measure, process, receive or transmit.

Before enters the sleeping mode, it verifies if it has neighbors

that use it as a router. If this does not occur, sleeps for seconds. If there are neighbors that use it as a router, then sleeps

for ,

= ( ) # (1)

and each represents the inactivity period of each neighbor of

. The sleeping period reduction factor (0 < < 1) is usedto increase the probability of being awake to forward packets

from its neighbors.

II-A. Algorithm 1

In Algorithm 1, a node only transmits samples that have a

percentage variation between the current measured one and the last

transmitted one that are larger than a predefined threshold . Thus,

after a node transmits the sample(), it only transmits the sample(+ ) if:

(+) ()

() (2)

If transmits()and

( +)at instants

()and

( +),

it calculates its inactivity period by eq. (3). The flow of

this algorithm is presented in Algorithm 1. In Algorithm 1,

978-1-4673-4900-0/13/$31.00 c2013 IEEE

8/12/2019 363-2631323

2/4

represents the current instant of measurement or transmission, is the energy of node , and we consider that nodes initially

have an inactivity period of 0.1 seconds, the timebase used in the

simulations. Moreover, line 3 ofAlgorithm 1 indicates that it runs

while node has energy, in consonance with the original concept

of network lifetime. (The same parameters are also considered inthe setup of Algorithm 2.)

= (+ )

()

2 (3)

Algorithm 1

1: n 12: 013: while > 0 do4: measures

()

5: ifn = 1 then6: transmits

()

7: ()8: () transmission instant9: ()

10: else

11: if ()

then

12: transmits ()

13: ()

14: () transmission instant

15: ()

2

16: ()17: if has packets to forward from # neighbors then

18: transmits packets from its Nneighbors

19: = (1 ) #

20: end if21: sleeps for = seconds22: wakes up after seconds

23: end if

24: end if

25: n n+126: end while

The sink node uses a zero order interpolator to reconstruct the

monitored process, i.e., one considers that the process does not vary

between the transmitted/received samples.

II-B. Algorithm 2

In Algorithm 2, each node , when computing the ,considers how the sink reconstructs the process from the measure-

ments that it receives. In doing so, one may impose an additional

constraint that is keeping the reconstruction error () to be smaller

than a given predefined threshold , that is, . One considersthat the sink node uses a first order interpolator to reconstruct the

process, i.e., the process varies linearly.

Suppose that a sensor node transmits its measured samples

to a sink node . generates a vector that contains the collected

measurements, s = [ (1)

(2)

()], and a vector

with the measuring instants, t = [ (1)

(2)

()]. At

the sink node, the reconstruction of the process is done from

the available information, a subset of the measured set vector,

generated from the received samples s and from their corre-

sponding instants t , i.e., s = [

(1)

(2)

()] and t

= [ (1) (2)

()]. The sink node uses s

and t

to

reconstruct the monitored field.

In this algorithm, we use a linear estimation: The last two

samples are considered to estimate a future transmission. Sensornodes can estimate a future measurement that will be transmitted

(+ 1) (and that is assumed to be received at sink node) suchthat , from measured samples, and from transmitted samples.The goal is the sensor nodes to be capable of estimating the time

interval between transmissions, in order to sleep and save energy.

We consider the following notation: For last two measured

samples and instants of measurements, we have ( 1) and ( 2),

( 1) and

( 2); for last two transmitted

samples and instants of transmissions, we have ( ) and(),

()and

(). We define the indexes

and for transmission, because not all measured samplesare transmitted. Furthermore, we define the following variations:

=

( 1)

( 2) (4) =

( 1)

( 2) (5)

= ()

( ) (6)

= ()

( ) (7)

and variation rates:

=

(8)

=

(9)

For this model, we consider that the transmitted and received sets

are equal. Thus, we want that the percentage variation between the

next transmission ( + 1) and the real value (+ 1) is less

than a given threshold (),

(+ 1) (+ 1)

(+ 1) (10)

Using a first order interpolation, we can estimate ( + 1) asfollows:

(+ 1) =( ) +(

()

()) (11)

with given by eq. (8). It is assumed that (+ 1) denotes the

next sample to be measured, thus (+ 1) = (). As

()

is not available, this value is estimated using the variation rate of

the monitored process, (), defined by:

() = ( 1) +(

()

( 1)) (12)

with defined by eq. (9). By this way, eq. (10) turns:

() + ( ()

())

()

() (13)

Replacing eq. (12) in (13), we obtain:

( )+( ()

()) (14)

( ( 1) +( ()

( 1)))

( 1) +( ()

( 1))

By solving inequation (14), the inactivity period of node can be estimated as the time interval between the last transmitted

sample and the future one.

= ()

() (15)

8/12/2019 363-2631323

3/4

The flow of this algorithm is presented in Algorithm 2.

Algorithm 2

1: n 12: 01

3: while > 0 do4: measures

()

5: ifn = 1 then6: transmits

()

7: else

8: transmits ()

9: calculates using linear estimation

10: if has packets to forward from # neighbors then

11: transmits packets from its # neighbors

12: = (1 ) #13: end if

14: sleeps for = seconds15: wakes up after seconds

16: end if

17: n n+118: end while

III. ENERGY MODEL AND SIMULATION ASPECTS

The energy model used in this work is a state-based model, in

which nodes may operate in two states: Inactive or active. The

inactive state (sleep mode) is an energy saving mode. The active

state is composed by four operation modes: Measuring, processing,

transmission, and receiving. The proposed energy model takes into

account the packet payload size, and it is based on [5], an empirical

energy model, obtained using the TELOS commercial hardware [6],

in which it is observed that the energy consumption and the packet

payload size are linearly related (in the transmission mode).The energy consumption of a node can be estimated, as

a function of the period of time in which the node stays in the

different operation modes.

= +

+ (+) + (+)

+ (+) + (+) (16)

in which,,,, and are, respectively, the cumulative

sum of intervals in which a node remains in inactive and active

states, and in measuring, processing, receiving, and transmitting

operation modes. If a node is active, there is an increment in its

energy consumption, depending on the task it is performing. The

associated consumptions of each one of the states and modes

are parameters that are presented in Table I.

The simulations were performed in TrueTime 1.5 [7], a sim-

ulation environment based in MatLab/Simulink and the network

standard considered was the IEEE 802.15.4 [8].For simulations, we considered monitoring a smooth process

modeled as surface ( ). The process, used to evaluate theestimator is described by eq. (17), in which and represent

the location of the monitored phenomenon, andit is the location

of its maximum; , and represent the confinement of the

sensed phenomenon in space; and is a constant.

( ) =

()

2

22 +

()2

22

()

2

22 + (17)

Table I. Static parameters of the simulations Cons. refers to

energy consumption.

Node initial energy (J) 2.00

Transmission power (dBm) -5

Reception sensibility (dBm) -66

Radio range (m) 40

: Inactive state Cons. (mJ/s) 1.80

: Active state Cons. (mJ/s) 10.00

: Measuring mode Cons. (mJ/s) 18.00

: Processing mode Cons. (mJ/s) 18.00

: Rx mode Cons. (mJ/s) 62.40

: Tx mode Cons. (mJ/s) 58.62

Payload size (Byte) 1

In this work, a multihop communication model is considered, in

which a routing protocol is used, in order to forward packets node-

to-node from sources to the sink. The Ad-hoc On Demand Distance

Vector (AODV) [9] routing protocol is considered in simulations.For the scenario, a WSN with fifteen nodes was used to sense a

8080region, in which sink node is positioned in the middleat the right and sensor nodes are randomly positioned. In each run

of simulation, the position of sink node is fixed, and the positions

of sensor nodes are randomly sorted.

IV. SIMULATION RESULTS

This section presents the results obtained. Each simulation was

run ten times, and a 95% confidence interval for the mean is used

in the graphs, represented by vertical bars. Thresholds () of 0.1%,

1.0%, 5.0% and 8.0% were considered. The following parameters

were considered, for the monitored process: = = =

40; = = = 20; and = 5. Moreover, we consider= 05 in the simulations.

Figure 1 shows the Cumulative Distributed Function (CDF) of

the reconstruction error of the monitored process, for different

thresholds, for Algorithm 1 and Algorithm 2. It represents the

probability of error () being less than a given threshold , i.e.,

( < ). In this figure, solid lines show the reconstructionerror with Algorithm 1, and the same metric for Algorithm 2

is presented by dashed lines. It can be observed an increase in

the reconstruction error with the increment of, as expected. This

increment of allows a larger percentage variation between the

measured sample and the last one transmitted.

As discussed in Section II, a constraint imposed by Algorithm 2

is that the reconstruction error should be smaller than the threshold.

It can be seen in Figure 1, that this constraint is satisfied. The samecondition is not observed in simulations with Algorithm 1. Thus,

Algorithm 2 leads to smaller reconstruction error than Algorithm

1 does.

Figure 2 shows the increase in the lifetime of the WSN, and

the decrease in the amount of transmissions, in function of .

These results were obtained comparing our proposal to a network

without any kind of energy management, in which nodes simply

take measures and transmit them periodically at each 0.1 seconds.

It can be observed that the increase of leads to the reduction in

the transmissions and to the increase in the network lifetime. To

increase the threshold means that nodes only transmit measured

samples for a greater percentage variation, because a larger re-

8/12/2019 363-2631323

4/4

construction error is allowed. Furthermore, nodes may have larger

sleeping periods, and they transmit fewer measurements.We also observe that Algorithm 1 leads to a grater increase in

the lifetime of the network than Algorithm 2 does. This is so,

because the first algorithm allows larger reconstruction error, and

this behavior is compatible with a tradeoff between the energyconsumption and the reconstruction of the process. Thus, for

different applications, it can be preferred to have a controlled

reconstruction of the monitored process at the expenses of the

lifetime of the network. However, as can be noted, both algorithms

lead to a significant energy saving.

0 5 10 15 20 25 300

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Reconstruction error (%)

Recon

structionerrorCDF

= 0.1%

= 1%

= 5%

= 8%

= 0.1%

= 1%

= 5%

= 8%

0 0.02 0.04 0.06 0.08 0.10

0.2

0.4

0.6

0.8

1

Fig. 1. Reconstruction error CDF of the monitored process with

Algorithm 1 and Algorithm 2.

0 1 2 3 4 5 6 7 80

500

1000

1500

(%)

Lifetimeincrease(%)

Algorithm 1

Algorithm 2

0 1 2 3 4 5 6 7 80

50

100

(%)Transmissiondecrease(%)

Algorithm 1

Algorithm 2

Fig. 2. Lifetime increase and decrease in the transmissions .

Table II shows the packet delivery ratio in function of, for bothalgorithms. This metric evaluates the connectivity of the network.

It is defined as the ratio between the amount of received and

transmitted packets. In the simulations, confidence intervals for

the means between 0.5% and 1.0% were obtained. We can see

that by increasing the threshold, there is a reduction in packet

delivery ratio. In Algorithm 2, nodes transmit more packets than

in Algorithm 1. This may lead to an increase in the probability of

collisions in the network, affecting the network connectivity more

than in Algorithm 1.

V. CONCLUSIONS

In this work, we propose two algorithms for energy conservation

in WSNs. The algorithms aim at reconstructing a process ( )

Table II. Packet delivery ratio .

0.1% 1.0% 5.0% 8.0%

Algorithm 1 98% 97% 88% 83%

Algorithm 2 89% 88% 87% 87%

with energy efficiency. This means that sensor nodes explore the

variation rate of the monitored process to reduce the amount of

transmissions, in order to increase the lifetime of the network.

Furthermore, nodes may enter in an inactivity mode between the

transmissions to save energy.

It can be observed that Algorithm 1 can reach a larger energy

conservation, but without keeping the reconstruction error less

that the predefined threshold. In Algorithm 2, this constraint is

respected, while obtaining significant increases in the network

lifetime.

VI. ACKNOWLEDGMENT

This work has been supported by FAPERJ, CAPES and CNPq.

VII. REFERENCES

[1] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci,Wireless Sensor Networks: A Survey, Computer Networks, vol.38, pp. 393422, 2002.

[2] A. Mainwaring, J. Polastre, R. Szewczy, and D. Culler, WirelessSensor Networks for Habitat Monitoring, in ACM InternationalWorkshop on Wireless Sensor Networks and Applications, Septem-ber 2002, pp. 8897.

[3] Z. M. Wang, S. Basagni, E. Melachrinoudis, and C. Petrioli, Ex-ploiting Sink Mobility for Maximizing Sensor Networks Lifetime,in Proc. 38th Annual Hawaii International Conference on SystemSciences (HICSS05), Hawaii, January 2005, pp. 36.

[4] V. K. Sachan, S. A. Imam, and M. T. Beg, Energy-efficient

Communication Methods in Wireless Sensor Networks: A CriticalReview, International Journal of Computer Applications, vol. 39,no. 17, February 2012.

[5] Y. Panthachai and P. Keeratiwintakorn, An Energy Model forTransmission in Telos-Based Wireless Sensor Networks, inProceedings of the 4th International Joint Conference on Computer

Science and Software Engineering, 2007.[6] J. Polsatre, R. Szewczyk, and D. Culler, Telos: Enabling Ultra-

Low Power Wireless Research, in Proceedings of the 4th Interna-tional Symposium on Information Processing in Sensor Networks,2005.

[7] A. Cervin, D. Herinksson, B. Lincoln, J. Eker, and K.-E. Arzen,How Does Control Timing Affect Performance?, IEEE ControlSystems Magazine, vol. 23, no. 3, pp. 1630, 2003.

[8] P. Baronti, P. Pillai, V. Chook, S. Chessa, A. Gotta, and Y. F. Hu,

Wireless Sensor Networks: a Survey on the State of Art and the802.15.4 and ZigBee Standards, Computer Communications, vol.30, no. 7, pp. 16551695, May 2007.

[9] C. Perkins, E. Belding-Royer, and S. Das, Ad Hoc On DemandDistance Vector Routing (AODV), in RFC 3561, July 2003.