Energy Efficiency Issues

8/15/2019 Energy Efficiency Issues

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Centre for WirelessCommunications

Wireless Sensor Networks

Energy Efficiency Issues

Instructor: Carlos Pomalaza-Rez

Fall 2004University of Oulu, Finland


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Node Energy Model

A typical node has a sensor system, A/D conversion circuitry, DSP and aradio transceiver. The sensor system is very application dependent. As

discussed in the Introduction lecture the node communication components

are the ones who consume most of the energy on a typical wireless sensor

node. A simple model for a wireless link is shown below


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Node Energy Model

The energy consumed when sending a packet of m bits over one hop

wireless link can be expressed as,

{ } { }decodestRRencodestTTL ETPmEETPdmEdmE +++++= )(),(),(

where,

ET = energy used by the transmitter circuitry and power

amplifier

ER = energy used by the receiver circuitry

PT = power consumption of the transmitter circuitryPR = power consumption of the receiver circuitry

Tst = startup time of the transceiver

Eencode = energy used to encode

Edecode = energy used to decode


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Node Energy Model

An explicit expression foreTA can be derived as,

))()((

4))()(( 0

bitampant

Rx

rTA

RG

BWNNFN

S

e

=

Where,(S/N)r = minimum required signal to noise ratio at the receivers

demodulator for an acceptableEb/N0NFrx =receiver noise figure

N0 = thermal noise floor in a 1 Hertz bandwidth (Watts/Hz)

BW = channel noise bandwidth = wavelength in meters

= path loss exponent

Gant = antenna gain

amp = transmitter power efficiency

Rbit = raw bit rate in bits per second


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Node Energy Model

The expression foreTA

can be used for those cases where a particular

hardware configuration is being considered. The dependence ofeTA on(S/N)r can be made more explicit if we rewrite the previous equation as:

( )))()((

4))()((

erewh0

bitampant

Rx

rTA

RG

BWNNF

NSe

==

It is important to bring this dependence explicitly since it highlights

how eTA

and the probability of bit errorp arerelated.p depends onEb/N

0

which in turns depends on (S/N)r. Note thatEb/N0is independent of thedata rate. In order to relateE

b/N

0to (S/N)

r, the data rate and the system

bandwidth must be taken into account, i.e.,


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Node Energy Model

( ) ( ) ( ) ( )TbTbr BRBRNENS == 0

where

Eb = energy required per bit of information

R = system data rate

BT = system bandwidth

b = signal-to-Noise ratio per bit, i.e., (Eb/N0)

2.0 x Bit RateBPSK, DBPSK, OFSK

1.5 x Bit RateMSK

1.0 x Bit RateQPSK, DQPSK

Typical Bandwidth

(Null-To-Null)Modulation Method

Typical Bandwidths for Various Digital Modulation Methods


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Node Energy Model

Power Scenarios

There are two possible power scenarios:

Variable transmission power. In this case the radio dynamically adjust its

transmission power so that (S/N)r is fixed to guarantee a certain level of

Eb/N0at the receiver. The transmission energy per bit is given by,

dN

Sde

rTA

==bitperenergyonTransmissi

Since (S/N)r is fixed at the receiver this also means that the probabilitypof bit error is fixed to the same value for each link.


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Node Energy Model

Fixed transmission power. In this case the radio uses a fixed power for all

transmissions. This case is considered because several commercial radiointerfaces have a very limited capability for dynamic power adjustments.

In this case is fixed to a certain value (ETA

) at the transmitter and the

(S/N)rat the receiver will then be,

deTA

d

E

N

S TA

r

=

Since for most practical deployments dis different for each link then(S/N)

rwill also be different for each link. This translates on a different

probability of bit error for wireless hop.


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Energy Consumption - MultihopNetworks

Lets consider the following linear sensor array

To highlight the energy consumption due only to the actual

communication process the energy spent in encoding, decoding, as well

as on the transceiver startup is not considered in the analysis that follows.

Lets initially assume that there is one data packet being relayed from the

node farthest from the sink node towards the sink


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The total energy consumed by the linear array to relay a packet ofm bits

from node n to the sink is then,

[ ] [ ]

[ ]

+++=

++++=

=

=

n

i

iTARCTCRC

n

i

iTARCTCTATClinear

deeeem

deeedeemE

1

2

1

)(

or

)()(

It then can be shown thatElinear is minimum when all the distances dis aremade equal toD/n, i.e. all the distances are equal.


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It can also be shown that the optimal number of hops is,

=

charchar

optd

D

d

Dn or

where

1

)1(

+=

TA

RCTCchar

eeed

Note that only depends on the path loss exponent and on the

transceiver hardware dependent parameters. Replacing the ofdchar in the

expression forElinearwe have,

+= RC

RCTCoptoptlinear e

eenmE

1

)(


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A more realistic assumption for the linear sensor array is that there is a

uniform probability along the array for the occurrence of events. In thiscase, on the average, each sensor will detect the same number of number

of events whose related information need to be relayed towards the sink.

Without loss of generality one can assume that each node senses an event

at some point in time. This means that sensori will have to relay (n-i)

packets from the upstream sensors plus the transmission of its own

packet. The average energyper bitconsumption by the linear array is,

( )( )[ ]

)()1(2

)1()(

1)(

1

1

i

n

i

TARCTC

RC

n

i

iTARCTCRCbitlinear

dinennee

ne

indeeeneE

=

=

+++++=

++++=


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bitlinearE ==n

iidD 1Minimizing with constraint is equivalent tominimizing the following expression,

( )[ ]

+=

==

DddineL

n

i

i

n

i

iTA

11

)(1

where is a Langrages multiplier. Taking the partial derivatives ofL

with respect to di and equating to 0 gives,

1

1

1

)1(

0))(1(

+

=

=+=

ined

dine

d

L

TA

i

iTA

i


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The value of can be obtained using the condition=

=n

i

i Dd

1

Thus for=2 the values fordiare,

( ) ( )ini

Dd

n

i

i

+

=

=

11

1

Forn=10 the next figure shows an equally spaced sensor array and a

linear array where the distances are computed using the equation above

(=2)


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The farther away sensors consume most of their energy by transmitting

through longer distances whereas the closer to the sink sensors consume alarge portion of their energy by relaying packets from the upstream sensors

towards the sink. The total energy per bit spent by a linear array with

equally spaced sensors is

( )( )RCTARCTCbitlinear nenDeee

nn

E ++

+

=2tequidistan

2

)1(

The total energy per bit spent by a linear array with optimum separation

and =2 is,

( )

( )RCn

i

TARCTCbitlinear ne

i

DeeennE +++=

=

1

2optimum

12

)1(


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ForeTC= eTR= 50 nJ/bit, eTA= 100 pJ/bit/m2, and = 2, the total energy

consumption per bit forD= 1000 m, as a function of the number of sensors

is shown below.

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0 5 10 15 20 25 30

Sensor Array Size (n )

Energy(m

J)

Equally spaced Optimum spaced


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The energy per bit consumed at node i for the linear arrays discussed can be

computed using the following equation. It is assumed that each node relays packet

from the upstream nodes towards the sink node via the closest downstream neighbor.For simplicity sake only one transmission is used, e.g. no ARQ type mechanism

])())(1[()( RCiTATClinear eindeeiniE +++=

0.0

2.0

4.0

6.0

8.0

0 5 10 15 20

Distance (hops) from the sink

Energy

(uJ)

Equally Spaced Optimum Spaced

Total Energy=72.5 uJ

Total Energy = 47.8 uJ

Energy consumption at each node (n=20,D=1000 m)


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Error Control Multihop WSN

For linki assume that the probability of bit error ispi

. Assume a packet

length ofm bits. For the analysis below assume that a Forward Error

Correction (FEC) mechanism is being used. Lets then callplink(i) the

probability of receiving a packet with uncorrectable errors. Conventional

use of FEC is that a packet is accepted and delivered to the next stage

which in this case is to forward it to the next node downstream. The

probability of the packet arriving to the sink node with no errors is then:

( )=

=n

i

linkc ipP1

)(1


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Error Control Multihop WSNLets assume the case where all the dis are the same, i.e. di =D/n. Since

variable transmission power mode is also being assumed then theprobability of bit error for each link is fixed and Pcis,

nlinkc pP )1( =

The value ofplink

will depend on the received signal to noise ratio as well

as on the modulation method used. For noncoherent (envelope or square-

law) detector with binary orthogonal FSK signals in a Rayleigh slow

fading channel the probability of bit error is

bFSKp += 2

1

Where is the average signal-to-noise ratio.b


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Error Control Multihop WSN

Consider a linear code (m, k, d) is being used. For FSK-modulation with

non-coherent detection and assuming ideal interleaving the probability ofa code word being in error is bounded by

( )min

2

2

12

d

b

M

i i

i

M

w

w

P

+

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Energy Efficiency Issues