Wireless Sensor Networks Energy Efficiency Issues

Centre for Wireless Communications

Wireless Sensor NetworksEnergy Efficiency Issues

Instructor: Carlos Pomalaza-Ráez

Fall 2004University of Oulu, Finland

Node Energy Model

A typical node has a sensor system, A/D conversion circuitry, DSP and a radio 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

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 amplifierER = energy used by the receiver circuitryPT = power consumption of the transmitter circuitryPR = power consumption of the receiver circuitryTst = startup time of the transceiverEencode = energy used to encodeEdecode = energy used to decode

Node Energy Model

Assuming a linear relationship for the energy spent per bit at the transmitter

and receiver circuitry ET and ER can be written as,

deemdmE TATCT ),(

RCR memE )(

eTC, eTA, and eRC are hardware dependent parameters and α is the path loss exponent whose value varies from 2 (for free space) to 4 (for multipath channel models). The effect of the transceiver startup time, Tst, will greatly depend of the type of MAC protocol used. To minimize power consumption it is desired to have the transceiver in a sleep mode as much as possible however constantly turning on and off the transceiver also consumes energy to bring it to readiness for transmission or reception.

Node Energy ModelAn explicit expression for eTA can be derived as,

))()((

4))()(( 0

bitampant

Rxr

TA RG

BWNNFN

S

e

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

demodulator for an acceptable Eb/N0

NFrx = receiver noise figureN0 = thermal noise floor in a 1 Hertz bandwidth (Watts/Hz)BW = channel noise bandwidthλ = wavelength in metersα = path loss exponent Gant = antenna gainηamp = transmitter power efficiencyRbit = raw bit rate in bits per second

Node Energy ModelThe expression for eTA can be used for those cases where a particular hardware configuration is being considered. The dependence of eTA on (S/N)r can be made more explicit if we rewrite the previous equation as:

))()((

4))()((

ere wh0

bitampant

Rx

rTA RG

BWNNFNSe

It is important to bring this dependence explicitly since it highlights how eTA and the probability of bit error p are related. p depends on Eb/N0

which in turns depends on (S/N)r. Note that Eb/N0 is independent of the

data rate. In order to relate Eb/N0 to (S/N)r, the data rate and the system

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

Node Energy Model TbTbr BRBRNENS 0

where

Eb = energy required per bit of informationR = system data rate

BT = system bandwidth

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

Modulation MethodTypical Bandwidth

(Null-To-Null)

QPSK, DQPSK 1.0 x Bit Rate

MSK 1.5 x Bit Rate

BPSK, DBPSK, OFSK 2.0 x Bit Rate

Typical Bandwidths for Various Digital Modulation Methods

Node Energy Model

Power ScenariosThere 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/N0 at the receiver. The transmission energy per bit is given by,

dN

Sde

rTA

bit per energy on Transmissi

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

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 radio interfaces 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)r at the receiver will then be,

deTA

d

E

N

S TA

r

Since for most practical deployments d is different for each link then (S/N)r will also be different for each link. This translates on a different

probability of bit error for wireless hop.

Energy Consumption - Multihop Networks

Let’s 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.

Let’s initially assume that there is one data packet being relayed from the node farthest from the sink node towards the sink


The total energy consumed by the linear array to relay a packet of m bits from node n to the sink is then,

n

iiTARCTCRC

n

iiTARCTCTATClinear

deeeem

deeedeemE

1

21

)(

or

)()(

It then can be shown that Elinear is minimum when all the distances di’s

are made equal to D/n, i.e. all the distances are equal.


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

charcharopt d

D

d

Dn or

where

1

)1(

TA

RCTCchar e

eed

Note that only depends on the path loss exponent α and on the transceiver hardware dependent parameters. Replacing the of dchar in the expression for Elinear we have,

RC

RCTCoptoptlinear e

eenmE

1

)(


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 this case, 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 sensor i will have to relay (n-i) packets from the upstream sensors plus the transmission of its own packet. The average energy per bit consumption by the linear array is,

)()1(2

)1()(

1)(

1

1

i

n

iTA

RCTCRC

n

iiTARCTCRCbitlinear

dinennee

ne

indeeeneE


bitlinearE

n

iidD

1

Minimizing with constraint is equivalent to minimizing the following expression,

DddineLn

ii

n

iiTA

11

)(1

where λ is a Langrage’s multiplier. Taking the partial derivatives of L with respect to di and equating to 0 gives,

1

1

1

)1(

0))(1(

ined

dined

L

TAi

iTAi


The value of λ can be obtained using the condition

n

ii Dd

1

Thus for α=2 the values for di are,

ini

Dd

n

i

i

111

For n=10 the next figure shows an equally spaced sensor array and a linear array where the distances are computed using the equation above (α=2)


The farther away sensors consume most of their energy by transmitting through longer distances whereas the closer to the sink sensors consume a large 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 nenDeeenn

E

2tequidistan

2

)1(

The total energy per bit spent by a linear array with optimum separation and α=2 is,

RCn

i

TARCTCbitlinear ne

i

Deee

nnE

1

2optimum

12

)1(


For eTC= eTR= 50 nJ/bit, eTA= 100 pJ/bit/m2, and α = 2, the total energy consumption per bit for D= 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 )

En

erg

y (m

J)

Equally spaced Optimum spaced


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

En

erg

y (u

J)

Equally Spaced Optimum Spaced

Total Energy=72.5 uJ

Total Energy = 47.8 uJ

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

Error Control – Multihop WSN

For link i assume that the probability of bit error is pi. Assume a packet

length of m bits. For the analysis below assume that a Forward Error Correction (FEC) mechanism is being used. Let’s then call plink(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

ilinkc ipP

1

)(1

Error Control – Multihop WSNLet’s assume the case where all the di’s are the same, i.e. di = D/n. Since variable transmission power mode is also being assumed then the probability of bit error for each link is fixed and Pc is,

nlinkc pP )1(

The value of plink 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

Error Control – Multihop WSNConsider a linear code (m, k, d) is being used. For FSK-modulation with non-coherent detection and assuming ideal interleaving the probability of a code word being in error is bounded by

min

2

2

12

d

b

M

i i

i

M

w

w

P

where wi is the weight of the ith code word and M=2k. A simpler bound is:

min)]1(4)[1( dFSKFSKM ppMP

For the multihop scenario being discussed here plink = PM and the probability of packet error can be written as:

ndFSKFSK

k

nM

nlinkce

pp

PpPP

})]1(4)[12(1{1

)1(1)1(11

min

Error Control – Multihop WSNThe probability of successful transmission of a single code word is,

)1( esuccess PP

Parameter Value

NFRx 10dB

N0 -173.8 dBm/Hz or 4.17 * 10-21 J

Rbit 115.2 Kbits

0.3 m

Gant -10dB or 0.1

amp 0.2

3

BW For FSK-modulation, it is assumed to be the same as Rbit

eRC 50nJ/bit

eTC 50nJ/bit

Radio parameters used to obtain the results shown in the next slides

Error Control – Multihop WSNThe expected energy consumption per information bit is defined as:

success

linearbitilinear Pk

EE

Parameters for the studied codes are shown in Table below, t is the error correction capability.

Code m k dmin Code rate t

Hamming 7 4 3 0.57 1

Golay 23 12 7 0.52 3

Shortened Hamming

6 3 3 0.5 1

Extended Golay

24 12 8 0.5 3


0 0.005 0.01 0.015 0.02 0.025 0.0329

30

31

32

33

34

35

36

37

38

Bit error probability

Me

ters

Characteristic distance

Characteristic distance, dchar, as a function of bit error probability

for non-coherent FSK modulation


0 0.005 0.01 0.015 0.02 0.025 0.032

2.2

2.4

2.6

2.8

3

3.2

3.4

3.6

3.8

4x 10

-5 Energy consumtion with number of hops =10

Bit error probability of the channel with FSK-mod.

En

erg

y co

nsu

mp

tion

pe

r u

sefu

l bit

(6,3,3)(7,4,3) code(23,12,7) code(24,12,8) code

D = 1000 m


0 0.005 0.01 0.015 0.02 0.025 0.030.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5x 10



En

erg

y co

nsu

mp

tion

pe

r u

sefu

l bit

(6,3,3)(7,4,3) code(23,12,7) code(24,12,8) code

D = 1000 m


0 0.005 0.01 0.015 0.02 0.025 0.031

1.5

2

2.5

3

3.5

4

4.5

5x 10



En

erg

y co

nsu

mp

tion

pe

r u

sefu

l bit

(6,3,3)(7,4,3) code(23,12,7) code(24,12,8) code

D = 1000 m


0 0.005 0.01 0.015 0.02 0.025 0.030.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

-5 Energy consumption of the (7,4,3) code

Bit error probability of the channel with non-coherent FSK-mod.

En

erg

y co

nsu

mp

tion

pe

r u

sefu

l bit

10 Hops30 Hops50 Hops60 Hops

D = 1000 m

0 0.005 0.01 0.015 0.02 0.025 0.030.5

1

1.5

2

2.5

3

3.5

4x 10

-5 Energy consumption of the (24,12,8) code

Bit error probability of the channel with non-coherent FSK-mod.

En

erg

y co

nsu

mp

tion

pe

r u

sefu

l bit

10 Hops30 Hops50 Hops60 Hops


D = 1000 m

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Wireless Sensor Networks Energy Efficiency Issues