Wireless Sensor Networks Energy efficents

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

1. Centre for Wireless
Communications
Wireless Sensor Networks
Energy Efficiency Issues
Instructor: Carlos Pomalaza-Ráez
Fall 2004
University of Oulu, Finland

2. 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

3. 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,
E
T
= energy used by the transmitter circuitry and
power amplifier
E
R
= energy used by the receiver circuitry
P
T
= power consumption of the transmitter circuitry
P
R
= power consumption of the receiver circuitry
T
st
= startup time of the transceiver
E
encode
= energy used to encode
E
decode= energy used to decode

4. Node Energy Model
Assuming a linear relationship for the energy spent per bit at the transmitter
and receiver circuitry E
T
and E
R
can be written as,
 

deemdmE
TATCT ),(
RCR memE )(
e
TC, e
TA, and e
RC 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, T
st
,
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.

5. Node Energy Model
An explicit expression for e
TA can be derived as,
))()((
4
))()((
0
bitampant
Rx
r
TA
RG
BWNNF
N
S
e

















Where,
(S/N)
r = minimum required signal to noise ratio at the receiver’s
demodulator for an acceptable E
b/N
0
NF
rx = receiver noise figure
N
0 = thermal noise floor in a 1 Hertz bandwidth (Watts/Hz)
BW = channel noise bandwidth
λ = wavelength in meters
α = path loss exponent
G
ant = antenna gain
η
amp
= transmitter power efficiency
R
bit
= raw bit rate in bits per second

6. Node Energy Model
The expression for e
TA can be used for those cases where a particular
hardware configuration is being considered. The dependence of e
TA on
(S/N)
r can be made more explicit if we rewrite the previous equation as:

))()((
4
))()((
ere wh
0
bitampant
Rx
rTA
RG
BWNNF
NSe












It is important to bring this dependence explicitly since it highlights
how e
TA and the probability of bit error p are related. p depends on E
b
/N
0
which in turns depends on (S/N)
r
. Note that E
b
/N
0
is independent of the
data rate. In order to relate E
b
/N
0
to (S/N)
r
, the data rate and the system
bandwidth must be taken into account, i.e.,

7. Node Energy Model
 
TbTbr
BRBRNENS 
0
where
E
b= energy required per bit of information
R= system data rate
B
T
= system bandwidth
γ
b
= signal-to-Noise ratio per bit, i.e., (E
b
/N
0
)
Modulation Method
Typical 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

8. 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
E
b/N
0 at the receiver. The transmission energy per bit is given by,

 d
N
S
de
r
TA 





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.

9. 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 (E
TA
) at the transmitter and the
(S/N)
r
at the receiver will then be,

de
TA

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.

10. 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

11. Energy Consumption - Multihop Networks
The total energy consumed by the linear array to relay a packet of m 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 that E
linear
is minimum when all the distances d
i
’s
are made equal to D/n, i.e. all the distances are equal.

12. Energy Consumption - Multihop Networks
It can also be shown that the optimal number of hops is,













charchar
opt
d
D
d
D
n or
where


1
)1(











TA
RCTC
char
e
ee
d
Note that only depends on the path loss exponent α and on the
transceiver hardware dependent parameters. Replacing the of d
char
in the
expression for E
linear
we have,










RC
RCTCoptopt
linear
e
een
mE
1
)(



13. Energy Consumption - Multihop Networks
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
i
TA
RCTC
RC
n
i
iTARCTCRCbitlinear
dine
nnee
ne
indeeeneE










14. Energy Consumption - Multihop Networks
bitlinear
E
 


n
i
idD
1
Minimizing with constraint is equivalent to
minimizing the following expression,
  








 

DddineL
n
i
i
n
i
iTA
11
)(1 

where λ is a Langrage’s multiplier. Taking the partial derivatives of L
with respect to d
i and equating to 0 gives,
1
1
1
)1(
0))(1(




















ine
d
dine
d
L
TA
i
iTA
i

15. Energy Consumption - Multihop Networks
The value of λ can be obtained using the condition 


n
i
iDd
1
Thus for α=2 the values for d
i
are,
 ini
D
d
n
i
i












11
1
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)

16. Energy Consumption - Multihop Networks
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
nenDeee
nn
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
D
eee
nn
E 





1
2
optimum
1
2
)1(

17. Energy Consumption - Multihop Networks
For e
TC= e
TR= 50 nJ/bit, e
TA= 100 pJ/bit/m
2
, 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)
E
n
e
r
g
y
(m
J
)
Equally spacedOptimum spaced

18. Energy Consumption - Multihop Networks
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
E
n
e
r
g
y
(u
J
)
Equally SpacedOptimum Spaced
Total Energy=72.5 uJ
Total Energy = 47.8 uJ
Energy consumption at each node (n=20, D=1000 m)

19. Error Control – Multihop WSN
For link i assume that the probability of bit error is p
i
. 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 p
link
(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
ipP
1
)(1

20. Error Control – Multihop WSN
Let’s assume the case where all the d
i
’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 P
c
is,
n
linkc
pP )1(
The value of p
link
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
b
FSKp


2
1
Where is the average signal-to-noise ratio.b


21. 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 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 w
i
is the weight of the ith code word and M=2
k
. A simpler bound is:
min
)]1(4)[1(
d
FSKFSKM ppMP 
For the multihop scenario being discussed here p
link
= P
M
and the
probability of packet error can be written as:
nd
FSKFSK
k
n
M
n
linkce
pp
PpPP
})]1(4)[12(1{1
)1(1)1(11
min



22. Error Control – Multihop WSN
The probability of successful transmission of a single code word is,
)1(
esuccess
PP 
Parameter Value
NF
Rx
10dB
N
0
-173.8 dBm/Hz or 4.17 * 10
-21
J
R
bit
115.2 Kbits
 0.3 m
G
ant
-10dB or 0.1

amp
0.2
 3
BW For FSK-modulation, it is assumed to be the same as R
bit
e
RC
50nJ/bit
e
TC
50nJ/bit
Radio parameters used to obtain the results shown in the next slides

23. Error Control – Multihop WSN
The expected energy consumption per information bit is defined as:
success
linearbiti
linear
Pk
E
E

Parameters for the studied codes are shown in Table below, t is the
error correction capability.
Code m kd
minCode ratet
Hamming 7 4 3 0.57 1
Golay 2312 7 0.52 3
Shortened
Hamming
6 3 3 0.5 1
Extended
Golay
2412 8 0.5 3

24. Error Control – Multihop WSN
0 0.005 0.01 0.015 0.02 0.025 0.03
29
30
31
32
33
34
35
36
37
38
Bit error probability
M
e
t
e
r
s
Characteristic distance
Characteristic distance, d
char
, as a function of bit error probability
for non-coherent FSK modulation

25. Error Control – Multihop WSN
0 0.005 0.01 0.015 0.02 0.025 0.03
2
2.2
2.4
2.6
2.8
3
3.2
3.4
3.6
3.8
4
x 10
-5
Energy consumtion with number of hops =10
Bit error probability of the channel with FSK-mod.
E
n
e
r
g
y

c
o
n
s
u
m
p
t
i
o
n

p
e
r
u
s
e
f
u
l
b
i
t
(6,3,3)
(7,4,3) code
(23,12,7) code
(24,12,8) code
D = 1000 m

26. Error Control – Multihop WSN
0 0.005 0.01 0.015 0.02 0.025 0.03
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
x 10
-5
Energy consumtion with number of hops =30
Bit error probability of the channel with FSK-mod.
E
n
e
r
g
y

c
o
n
s
u
m
p
t
i
o
n
p
e
r
u
s
e
f
u
l
b
i
t
(6,3,3)
(7,4,3) code
(23,12,7) code
(24,12,8) code
D = 1000 m

27. Error Control – Multihop WSN
0 0.005 0.01 0.015 0.02 0.025 0.03
1
1.5
2
2.5
3
3.5
4
4.5
5
x 10
-5 Energy consumtion with number of hops =60
Bit error probability of the channel with FSK-mod.
E
n
e
r
g
y
c
o
n
s
u
m
p
t
io
n
p
e
r

u
s
e
fu
l
b
it
(6,3,3)
(7,4,3) code
(23,12,7) code
(24,12,8) code
D = 1000 m

28. Error Control – Multihop WSN
0 0.005 0.01 0.015 0.02 0.025 0.03
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
x 10
-5
Energy consumption of the (7,4,3) code
Bit error probability of the channel with non-coherent FSK-mod.
E
n
e
r
g
y

c
o
n
s
u
m
p
tio
n
p
e
r
u
s
e
fu
l b
i
t
10 Hops
30 Hops
50 Hops
60 Hops
D = 1000 m

29. 0 0.005 0.01 0.015 0.02 0.025 0.03
0.5
1
1.5
2
2.5
3
3.5
4
x 10
-5
Energy consumption of the (24,12,8) code
Bit error probability of the channel with non-coherent FSK-mod.
E
n
e
r
g
y

c
o
n
s
u
m
p
ti
o
n
p
e
r
u
s
e
f
u
l
b
it
10 Hops
30 Hops
50 Hops
60 Hops
Error Control – Multihop WSN
D = 1000 m