Information Technology Reference

In-Depth Information

E

=

H

×

n

[

n

+

n

×

0

75

]

×

p

ham

2

pac

bits

bits

h

2

where
H
can be evaluated
H=3
,
n
bits
is the number of bits of the HAM2 packet and
p
h2
is the

probability that the AUX2 packet arrives correctly at the receiver after the second hop

(because the packet will be discarded if the CRC detects errors):

(

)
2

p

=

1

−

PER

h

2

f

The total energy consumed by DH1 packet is

[

]

E

=

H

×

n

×

N

×

n

+

n

×

0

.

75

×

p

dh

1

pac

bits

bits

h

5

where
H
is the number of the remaining hops of the network,
n
bits
is the number of bits of the

DH1 packet and
p
h5
is the probability that the HAM2 packet arrives correctly at the receiver

after the fifth hop, given by:

(

)

3

p

=

1

−

PER

×

p

h

5

f

h

2

The number of transmitted packets with error is the sum of errors occurred in the

transmissions of the AUX2 and HAM2 packets, as the DH1 packet will always be

retransmitted until it is correctly received:

n

=

n

+

n

error

error

_

aux

2

error

_

ham

2

The number of errors of the AUX2 packet is the product of the total number of

transmitted packets
n
pac
and the probability of error of the AUX2 packet in two hops:

2

n

=

[

−

(

−

PER

)

]

×

n

error

_

aux

2

f

pac

The number of errors of the HAM2 packet has the same form, but the number of errors

occurred in the first and second hops using the AUX2 packet have to be subtracted from the

total number of transmitted packets
n
pac
:

3

n

=

[

−

(

−

PER

)

]

×

(

n

−

n

)

error

_

ham

2

f

pac

error

_

aux

2

Then the reliability and the energy efficiency can be evaluated. For the ADP2 scheme,

the energy efficiency may be evaluated using the same equations of ADP1 scheme, replacing

the HAM2 packet by the BCH2 packet.