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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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Energy Consumption - MultihopNetworks
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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Energy Consumption - MultihopNetworks
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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Energy Consumption - MultihopNetworks
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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Energy Consumption - MultihopNetworks
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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Energy Consumption - MultihopNetworks
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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Energy Consumption - MultihopNetworks
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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Energy Consumption - MultihopNetworks
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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Energy Consumption - MultihopNetworks
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
+