energy level performance of packet delivery schemes in wireless sensor networks in presence of...

8/13/2019 Energy Level Performance of Packet Delivery Schemes in Wireless Sensor Networks in Presence of Rayleigh Fadin

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Energy Level Performance of Packet Delivery Schemes in Wireless Sensor Networks

in Presence of Rayleigh Fading Channel

Arnab NandiDepartment of ECE

National Institute of Technology, Durgapur

Durgapur- 713209, India

[email protected]

Sumit Kundu, Member IEEEDepartment of ECE

National Institute of Technology, Durgapur

Durgapur- 713209, India

[email protected]

Abstract This paper evaluates energy level performance of

three packet delivery schemes in a Wireless Sensor Networks

(WSN) in presence of Rayleigh fading. Three different

information delivery mechanisms are investigated using

regenerative relays with or without error correction capability.

Energy consumption for successful delivery of a data packet

for each mechanism is evaluated and compared under severalconditions of node density, bit rate, transmit power etc. Energy

efficiency of different retransmission schemes are evaluated.

Further an optimal packet length based on energy efficiency is

derived.

Keywords-Wireless Sensor Networks; BER; Rayleigh fading,

ARQ.

I. INTRODUCTION

Most of the research work on WSN assumes idealizedradio propagation models without considering fading andshadowing effects. However network performance degradesdue to shadowing and fading [1]. Relayed transmission is a

promising technique that helps in attaining broader coverageand in combating the impairment of the wireless channel.Relaying information on several hops reduces the need oflarge transmitter power and distributes the use of powerthroughout the hops which results in extended battery lifeand lowered level of interference [2]. Energy conservation isone of the most important issues in WSN, where nodes arelikely to rely on limited battery power. The connectivity ofWSN mostly depends on the transmission power of thesource nodes. If the transmission power is not sufficientlyhigh there may be single or multiple link failure. Furthertransmitting at high power reduces the battery life andintroduces excessive inter node interference. Given that thesensors have limited energy, buffer space, and other

resources, different MAC protocols are being developed byseveral researchers [3, 4]. Most of the previous researchwork in this field assumes free-space radio link model andAdditive White Gaussian Noise (AWGN) [5-7]. Howeversignal fading due to multipath propagation severely impairsthe performance of wireless link. Several approaches havebeen proposed in literature to prolong network lifetime.Sooksan et al. evaluated Bit Error Rate (BER) performanceand optimal power to preserve the network connectivityconsidering only path-loss and thermal noise [5]. In [6]Bettstetter et al. derived the transmission range for which

network is connected with high probability considering free-space radio link model. In [7] the relationships betweentransmission range, service area and network connectednessis studied in a free space model. Narayanaswamy et al. [8]proposed a protocol that extends battery life throughproviding low power routes in a medium with path loss

exponent greater than two. In [9] a new method is proposedutilizing a diversity scheme to reduce power consumption inlarge scale sensor networks

In this paper energy level performance of three differentinformation delivery mechanisms are considered in presenceof Rayleigh fading. In all the three schemes, message packetis sent on hop-by-hop basis. Further in scheme I message iscorrected at every hop. While in the other two schemes,message is corrected at the destination. However in case II,ACK/NACK propagates from destination to source viamultiple hops through intermediate nodes but in case III itpropagates directly. Further we derived energy efficiency ofthose retransmission mechanisms. The energy requirementalso depends on routing and the Medium Access Control(MAC) protocol used [10-11]. Energy requirement forsuccessful delivery of a packet is evaluated under severalconditions of network such as node density. Impact ofRayleigh fading on energy requirement is also investigated.

The rest of the following paper is organized as follows:In Section II, we describe the system model that is used inthe derivation of energy consumption of three differentinformation delivery mechanisms over Rayleigh fadingchannel. In Section III, we describe the simulation model.Section IV shows simulation results and discussions. Finallyconclusions are drawn in Section V.

II. SYSTEM MODEL

A square grid network architecture is considered as in[5]. Fig. 1 shows a two tier sensor network using square gridtopology [5, 12]. Distance between two nearest neighbor isdlink. It is assumed that N numbers of nodes are distributedover a region of area A obeying square grid topology. The

node spatial density sq is defined as number of nodes per

unit area i.e., ANsq = . The minimum distance between

two consecutive neighbors is given by [5]

sq

linkd

1= (1)

2010 International Conference on Computational Intelligence and Communication Systems

978-0-7695-4254-6/10 $26.00 2010 IEEE

DOI 10.1109/CICN.2010.53

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Fig. 1: Sensor nodes in square grid topology

When the node density increases, minimum distancebetween two nodes decreases following (1).

Here we assume a simple routing strategy such that apacket is relayed hop-by-hop, through a sequence of nearestneighboring nodes, until it reaches the destination [10].Therefore, we assume that a route between source anddestination exists.

Further we consider a simple reservation-based MACprotocol, called reserve-and-go (RESGO) following [10-11].In this protocol, a source node first reserves intermediatenodes on a route for relaying its packets to the destination.A transmission can begin after a route is discovered andreserved. If the destination node is busy, it waits for anexponential random back-off time before transmitting orrelaying each packet again. When the random back-off timeexpires, node starts transmitting a packet. The random back-off time helps to reduce interference among nodes in thesame route and also among nodes in different routes.Throughout this paper, we assume that the random back-off

time is exponential with meant1 , where tis the packet

transmission rate.The major perturbations in wireless transmission are

large scale fading and small scale fading [1, 13]. Large scalefading represents the average signal power attenuation orpath loss due to motion over large areas. This phenomenonis affected by prominent terrain contours (hills, forests,billboards, clumps of buildings, etc.) between thetransmitter and receiver. However small-scale fadingexhibits rapid changes in signal amplitude and phase as aresult of small changes (as small as a half-wavelength) inthe spatial separation between a receiver and transmitter.The rate of change of these propagation conditions accountsfor the fading rapidity. Small-scale fading is also calledRayleigh fading because if the multiple reflective paths are

large in number and there is no line-of-sight signalcomponent, the envelope of the received signal isstatistically described by a Rayleigh pdf given below

( ) 222 2exp rrrp = for 0r 0= otherwise (2)

here r is the envelope amplitude of the received signal and22 is the pre-detection mean power of the multipath

signal. When there is a dominant non-fading signal

component present, the small scale fading envelope isdescribed by a Rician pdf. In the present work we considerthe presence of Rayleigh fading in addition to path loss.

It can be assumed without loss of generality that sourcenode is at the center of the network (see Fig. 1). If adestination node is selected at random, the minimumnumber of hops to reach the destination can vary from 1 to

2imax, where imax is the maximum tier order. Counting thenumber of hops on a route from the source to eachdestination node and finding the average value wedetermine the average number of hops. Assuming that eachdestination is equally likely, the average number of hops ona route can be written as [5]

2Nnhop (3)

The received signal at the receiver is the sum of threecomponents (i) the intended signal from a transmitter, (ii)interfering signals from other active nodes, and (iii) thermalnoise. Since the interfering signals come from other nodes,we assume that total interfering signal can be treated as anadditive noise process independent of thermal noise process.The received signal in the antenna, Y during each bit periodcan be expressed as [5]

thermal

N

j

jrcv nShSY ++=

=

2

1

(4)

where h is the channel on the receive antenna, Srcv is thedesired signal in the antenna, Sjis the interference from theother nodes and nthermalis the thermal noise signal.

The power received at the receiving end is given byFriis transmission equation [1]

( ) linkc

rtt

rcv df

cGGPP

22

2

4= (5)

where Pt is the transmit power, Gt is the transmittingantenna gain, Gr is the receiving antenna gain, fc is thecarrier frequency, is the path-loss exponent and c is thevelocity of light. Here we considered omni directional(Gt=Gr=1) antennas at the transmitter and receiver. Thecarrier frequency is in the unlicensed 2.4 GHz band.Assuming Binary Phase Shift Keying (BPSK) modulation,there can be two cases for the amplitude of the Srcv

bitbit

rcvrcv E

R

PS == for a 1+ transmission

bitbit

rcv ER

P== for a 1 transmission (6)

where Rbitis the bit rate and bitE is the bit energy of the

received signal considering only path loss.The interference power received from node j can be

written using Friis transmission equation [1, 5]

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( )j

rcvj

PP =int (7)

j is the multiplicative factor depends on the position of

the interfering node. It is observed that the significant partof the inter-node interference comes from the first two tires

only. So we consider inter-node interference from first twotires only.For each interfering node j, the amplitude of the

interfering signal can be of three types [5]:

bit

j

jR

PS

int= for a 1+ transmission

bit

j

R

Pint= for a 1 transmission

0= for no transmission of node j (8)

The probability that an interfering node will transmit andcause interference depends on the MAC protocol used.

Considering the RESGO MAC protocol and assuming thateach node transmits packets with length Lpkt, theinterference probability is equal to the probability that aninterfering node transmits during the vulnerable interval of

duration bitpkt RL . This probability can be written as [11]

bit

pktt

R

L

trans ep

=1 (9)

Thus Sjappears with different probabilities of transmissionas given below

bit

jj

R

PS

int= with probability transP

2

1

bit

j

R

Pint= with probability transP

2

1

0= with probability ( )transP1 (10)

Size of the interference vectorjS

increases as the number of

nodes increases in the network. The thermal noise powercan be written as

BFkTPthermal 0= (11)

where F is the noise figure, KJk /1038.123

= is the

Boltzmanns constant, T0is the room temperature and B isthe transmission bandwidth. The received thermal noisesignal is simply

BFkTnthermal 0= (12)

Next we derive the energy spent in successfullytransmitting a data packet considering three differentretransmission schemes between a pair of source and

destination nodes. Fig. 2 shows three different packetdelivery mechanisms.

Fig. 2: Different Information Delivery Mechanisms

Scheme I is based on hop-by-hop retransmission, asshown in Fig.2a following [14], where at every hop thereceiver checks the correctness of the packet and requestsfor a retransmission with a NACK packet to previous nodeuntil a correct packet is received. ACK packet is sent to thetransmitter indicating a successful transmission.

Scheme II is based on multi-hop delivery withintermediate nodes, performing as digital repeaters [15] asshown in Fig.2b. The packet is checked only at destinationfor correctness; retransmissions are requested to source,with a NACK coming back from destination to source via

intermediate nodes through multi-hop path.Scheme III is based on multi-hop delivery with

intermediate nodes, performing as digital repeaters [14] asshown in Fig.2c. The packet is checked at the destination forcorrectness. However retransmissions are requested tosource, with a NACK coming back to source directly fromdestination (without multi-hop).

It is assumed that each packet consists of header,message and trailer as shown in Fig. 3. So, transmittedpacket length can be expressed as [16],

tmhpkt lllL ++= (13)

Fig. 3. Simple structure of a packet

where hl , ml and tl are the header length, message length

and trailer length respectively. So, the energy required totransmit a single packet is

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bit

pktt

tR

LPE = (14)

Here it is assumed that 75% of the transmit energy isrequired to receive a packet [17]. So, energy required tocommunicate, i.e. transmit and receive a single packet isgiven by

dbit

ackpktt

packet ER

lLPE +

+

= 75.1)(

(15)

where Edis the decoding energy to decode a single packetand lack is the acknowledge frame length. Since ForwardError Correction (FEC) technique is not used here, decodingenergy and trailer length both are assumed zero [16]. Thusthe energy to communicate a single packet is:

75.1)(

++=

bit

ackmhtpacket

R

lllPE (16)

The minimum energy required to communicate a packetis the energy required to transmit and receive the message

bits (lm) only. Thus minimum energy is given by thefollowing expression:

75.1min =bit

mt

R

lPE (17)

Now we consider the energy requirement for threedifferent information delivery mechanisms as mentionedabove to communicate a data packet from source todestination node until it is received successfully.

Scheme I:

Average probability of error at packet level at each hopis expressed as [17]

pktL

linklink BERPER )1(1 = (18)

Where, BERlink is the link BER in presence of Rayleighfading. The probability of n retransmissions is the productof failure in the (n-1) transmissions and the probability ofsuccess at the nthtransmission:

1))(1(][ = nlinklinkI PERPERnP (19)

Average number of retransmissions for scheme I, assumingan infinite ARQ

( )link

link

n

IIPER

PERnnPR

==

=

1].[

1

(20)

We consider only path loss in reverse link. Further weassume that ACK/NACK from receiving node isinstantaneous and error free. Considering receiversensitivity Si, the required transmit power for reverse link isgiven by [1]

( )2

224

cGG

dfSP

rt

linkitI

= (21)

The energy consumed per packet at the end ofhopn number

of hops is considered as the energy spent in forwardtransmission of information and reverse transmission forNACK/ACK as in [17]

[ ]acktImhtbit

hopI

I lPllP

R

nRE )(

)1(75.1++

+

= (22)

Scheme II:

Average probability of error at packet level at the end ofmultihop route is given as

hopn

linkroute PERPER )1(1 = (23)

Average number of retransmissions for scheme II is givenby

( )route

route

n

IIIIPER

PERnnPR

==

=1

].[

1

(24)

where PII[n] is the probability of n retransmissionsconsidering Scheme II. The energy consumed per packet at

the end of hopn number of hops is given by

[ ]acktIImhtbit

hopII

II lPllPR

nRE ++

+

= )()1(75.1

(25)

Where PtIIis the transmit power of reverse link and same asPtI.

Scheme III:

The energy consumed per packet at the end of

hopn number of hops using Scheme III is given by

[ ]acktIIImhtbit

hopIII

III lPllPR

nRE +++= )()1(75.1 (26)

where average number of retransmissions, RIII is same asRII. Reverse link transmit power PIIIis given as

( )2

224

cGG

dfSP

rt

avgi

tIII

= (27)

where davg is the average distance between source anddestination.

Now the energy efficiency () of each scheme can beexpressed as [17] :

Schemefor thatRequiredEnergy

minE= (28)

III. SIMULATION MODEL

We now present our simulation model developed inMATLAB to evaluate the performance of three differentinformation delivery mechanisms:

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At first digital data 1 and 0 with equal probability isgenerated for BPSK modulation. Our transmitted signalis +1 or -1 corresponding to data 1 or 0.

The desired message signal is affected by Rayleighfading, thermal noise and interference from othernodes. The signal received by the receiving antenna indestination node is generated following (4).

Rayleigh distributed random variables with 0 mean andnormalized variance 1 is generated to indicate thechannel.

The received signal Y as given in (4) is then detectedconsidering the threshold level at 0. If the receivedsignal is greater than the threshold level 0 then it isdetected as 1. Otherwise it is detected as 0.

Each received bit is then compared with the transmittedbits. If there is mismatch an error counter isincremented. Now dividing the error count by the totalnumber of transmitted bits, link BERs is obtained.

The energy efficiency for three information deliverymechanisms is evaluated using equn. (28).

The energy consumption of the three retransmissionschemes is evaluated using equn. (22), (25) and (26).

IV. RESULTS AND DISCUSSION

Table 1 shows the important network parameters used in thesimulation study

TABLE 1

Network Parameters used in the Simulation

Parameter Values

Path loss exponent () 2

Number of nodes in the network (N) 289

Node spatial Density (s) 10-9 10-2

Packet arrival rate at each node (t) 0.5 pck/s

Career frequency (fc) 2.4 GHzNoise figure (F) 6dB

Room Temperature (T0) 300k

Transmission Power (PTx) 10 mW, 100 mW

Receiver Sensitivity (Si) -60 dBm

Fig. 4 shows the link BER, denoted as BERlink fordifferent values of node spatial density considering differentbit rates and transmit power over a Rayleigh faded channel.It is observed that BERlink performance improves with theincrease in node spatial density. However it is seen thatbeyond a certain node density the BERlink does not changewith further increase in node spatial density and a floor inBERlink, as denoted by BERfloorappears. The desired signal

power as well as the inter-node interference increases withincrease in node density. As a result we obtain the BERfloor.This is expected because, increasing node spatial densitybeyond a certain limit no longer improves the signal to noiseratio (SNR), as the interfering nodes also become closeenough to the receiver. It is also seen that BERlinkperformance degrades as bit rate decreases. This is due toincrease in vulnerable interval with decrease of bit rate [5].As a result, transmission probability of the interfering nodes

Fig. 4. Link BER as a function of Node Spatial Density for different bit rateand transmit power.

increases. For a data rate of 10 Mbps and node spatial

density of 10-4

BERlink is 4109.3

, while it increases to31015.3

for a bit rate of 2 Mbps. Further it is observed

that BER floor appears earlier with the increase in transmitpower for a fixed bit rate.

Fig. 5 shows the energy efficiency as a function ofpacket length for different information deliverymechanisms. It is seen that there exists a peak value ofefficiency for a given packet size. The message lengthcorresponding to maximum efficiency is optimal packet sizefrom energy efficiency perspective [16]. Thus there existsan optimal packet size for a particular network condition.Further optimal packet length increases with the increase innode spatial density. For example, in case of scheme II at

node density of 61012.6 , optimal packet size is 56 bit but

it increase to 71 bit when node density increases to 4103 .

It is seen that the energy efficiency shows a steep drop formessage lengths smaller than the optimal length. This

Fig. 5. Energy efficiency as a function of packet length for different

retransmission schemes; Pt=100 mW.

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Fig. 6. Energy consumption to communicate a packet of length 100 bit vsnode spatial density for different retransmission schemes; Rbit=10 Mbps

and Pt=100 mW.

behavior can be attributed to the higher overhead and start-

up energy consumption of smaller packets [16]. On the otherhand, for message length larger than the optimal length, thedrop in energy efficiency is much slower due to increase inaverage retransmission. With the increase of packet lengththe vulnerable interval increases and the probability oftransmission of an interfering node becomes high. It isobserved that energy efficiency degrades in presence ofRayleigh fading. Further energy efficiency improves withincrease in node spatial density. It is seen that Scheme I isthe most energy efficiency information delivery system. Thisis because in case of Scheme I, average numberretransmission is less compared to other two schemes.Further among the three retransmission schemes, Scheme Ihas the highest optimum packet size.

Fig. 6 shows the energy required to successfully delivera fixed packet of size of 100 bit considering three differentinformation delivery mechanisms. Energy consumption inpresence of Rayleigh fading is compared with that of pathloss case only. It is seen that in presence of Rayleigh fadingenergy requirement increases. Further it is observed thatscheme I is the best retransmission scheme in energyconsumption perspective. Further it is observed that SchemeI and Scheme II consume nearly same amount of energy inhigh node density region. However Scheme II performsbetter in low node spatial density region. For example inpresence of Rayleigh fading and at a node density of

6106 , required energy to communicate 100 bit of data is

50 J for Scheme II while it is 95 J for Scheme III.

V. CONCLUSION

In this paper we have evaluated the energy levelperformance of three information delivery schemes. Asimulation test bed has been developed to assess theperformance of such network in terms of energyconsumption and bit error rate. Energy consumption usingthree different types of information delivery schemes arestudied and compared. It is seen that Scheme I performsbetter than the other two schemes. Further Scheme II

consumes less energy than Scheme III in low node densityregion. It is also seen that Scheme I provides highest energyefficiency compared to other schemes. An optimum packetlength, which maximizes energy efficiency is also is alsoderived. It is seen that optimal packet length increases withthe increase in node spatial density. Further it is observedthat scheme I yields highest size of optimum packet

compared to other two schemes. Decoding andretransmission for error correction at every node in multi-hop path seems to be more energy efficient compared toother mechanisms. The analysis is useful in designing anenergy efficient Wireless Sensor Network.

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