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E
=
H
×
n
×
N
×
(
n
+
n
×
0
75
+
n
+
n
×
0
75
)
pac
bits
bits
ack
ack
where n ack is the total number of bits of the return packet. In order to evaluate the energy E for
the packets without ARQ and with CRC (AUX2, BCH3 and HAM2 packets) the average
number of hops has to be computed. The probability that a packet achieves h hops is the
product of success in the h-1 hops and the probability of failure in the h th hop, if h<H . If h=H
the probability of a packet achieving H hops is the product of success in the h-1 hops and the
probability of failure in the h th hop added to the probability of success in the H hops:
[
]
h
1
p
[
h
]
=
(
PER
)
(
PER
)
,
if
h
<
H
H
f
f
[
]
1
p
[
h
]
=
(
PER
)
h
(
PER
)
+
(
PER
)
h
,
if
h
=
H
H
f
f
f
Therefore, the average number of hops H can be evaluated as:
= H
h
=
H
p
[
h
]
×
h
H
1
Then the total energy consumed E for the packets with CRC and without ARQ is:
(
)
E
=
H
×
n
×
n
+
n
×
0
.
75
pac
bits
bits
For a Bluetooth ad hoc network to be considered energy efficient, the maximum amount
of data bits has to be transmitted with the minimum energy consumption. An energy
efficiency parameter η may be defined as:
E
η
=
min
×
R
E
The energy efficiency for an adaptive scheme is evaluated using this equation, but the
energy E and the reliability R have to be evaluated in a different manner. For the ADP1
scheme the AUX2 packet is used for the first and second hops, the HAM2 packet for the
third, fourth and fifth hops and DH1 packet for the remaining hops of the sensor network. The
total energy E is the energy consumed by the different packets:
E
=
E
+
E
+
E
aux
2
ham
2
dh
1
The ene rg y consumed by the AUX2 packet is:
[
]
E
=
H
×
n
n
+
n
×
0
.
75
aux
2
pac
bits
bits
where the average number of hops H can be evaluated using H=2 and n bits is the number of
bits of the AUX2 packet. The energy consumed by the HAM2 packet is:       Search WWH ::

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