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Wireless Sensor NetworksEnergy Efficiency Issues

- Instructor Carlos Pomalaza-RáezFall

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,

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

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.

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

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.,

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

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

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.

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.

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

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.

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,

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,

Energy Consumption - Multihop Networks

where ? is a Langrages multiplier. Taking the

partial derivatives of L with respect to di and

equating to 0 gives,

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)

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,

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.

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)

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

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.

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

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 nexts

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

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.

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

Error Control Multihop WSN

Characteristic distance, dchar, as a function of

bit error probability for non-coherent FSK

modulation

Error Control Multihop WSN

D 1000 m

Error Control Multihop WSN

D 1000 m

Error Control Multihop WSN

D 1000 m

Error Control Multihop WSN

D 1000 m

Error Control Multihop WSN

D 1000 m

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