Wireless Sensor Networks Energy Efficiency Issues

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Wireless Sensor NetworksEnergy Efficiency Issues

• Instructor Carlos Pomalaza-RáezFall
  2004University of Oulu, Finland

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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
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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,
where, ET energy used by the transmitter
circuitry and power amplifier ER energy used
by the receiver circuitry PT power consumption
of the transmitter circuitry PR power
consumption of the receiver circuitry Tst startu
p time of the transceiver Eencode energy used
to encode Edecode energy used to decode
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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,
eTC, eTA, and eRC are hardware dependent
parameters and a 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.
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Node Energy Model
An explicit expression for eTA can be derived as,
Where, (S/N)r minimum required signal to noise
ratio at the receivers demodulator for an
acceptable Eb/N0 NFrx receiver noise
figure N0 thermal noise floor in a 1 Hertz
bandwidth (Watts/Hz) BW channel noise
bandwidth ? wavelength in meters a 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 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
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.,
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Node Energy Model
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)
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/N0 at the receiver. The transmission
  energy per bit is given by,

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.
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Node Energy Model
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.
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Energy Consumption - Multihop Networks
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 - 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,
It then can be shown that Elinear is minimum when
all the distances dis are made equal to D/n,
i.e. all the distances are equal.
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Energy Consumption - Multihop Networks
It can also be shown that the optimal number of
hops is,
where
Note that only depends on the path loss exponent
a and on the transceiver hardware dependent
parameters. Replacing the of dchar in the
expression for Elinear we have,
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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,
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Energy Consumption - Multihop Networks
where ? is a Langrages multiplier. Taking the
partial derivatives of L with respect to di and
equating to 0 gives,
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Energy Consumption - Multihop Networks
Thus for a2 the values for di are,
For n10 the next figure shows an equally spaced
sensor array and a linear array where the
distances are computed using the equation above
(a2)
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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
The total energy per bit spent by a linear array
with optimum separation and a2 is,
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Energy Consumption - Multihop Networks
For eTC eTR 50 nJ/bit, eTA 100 pJ/bit/m2, and
a 2, the total energy consumption per bit for
D 1000 m, as a function of the number of sensors
is shown below.
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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
Energy consumption at each node (n20, D1000 m)
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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.
Lets 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
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Error Control Multihop WSN
Lets 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 the
probability of bit error for each link is fixed
and Pc is,
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
Where is the average signal-to-noise ratio.
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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
of a code word being in error is bounded by
where wi is the weight of the ith code word and
M2k. A simpler bound is
For the multihop scenario being discussed here
plink PM and the probability of packet error
can be written as
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Error Control Multihop WSN
The probability of successful transmission of a
single code word is,
Radio parameters used to obtain the results
shown in the next slides
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Error Control Multihop WSN
The expected energy consumption per information
bit is defined as
Parameters for the studied codes are shown in
Table below, t is the error correction
capability.
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Error Control Multihop WSN
Characteristic distance, dchar, as a function of
bit error probability for non-coherent FSK
modulation
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Error Control Multihop WSN
D 1000 m
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Error Control Multihop WSN
D 1000 m
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Error Control Multihop WSN
D 1000 m
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Error Control Multihop WSN
D 1000 m
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Error Control Multihop WSN
D 1000 m