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Figure 3. Multi-hop ad hoc network.
The probability of a packet being successfully received at the receiver node is the
probability of success of the packet at forward and reverse channels :
PA
=
(
PER
)(
1
PER
)
f
r
Thus, the packet error probability for ARQ packets is:
PER
=
1
[(
1
PER
)(
1
PER
)]
f
r
This expression can be rewritten as:
PER
=
PER
+
PER
(
PER
)(
PER
)
f
r
f
r
The probability of a packet being successfully received at the sink node for the packets
without ARQ is:
P
=
( −
PER
)
H
narq
f
where H is the total number of hops. Let n be the number of retransmissions of ARQ
packets. Assuming perfect error detection of the CRC code and infinite retransmissions, the
probability that a packet arrives correctly at the sink node is:
H
=
=
[
]
P
p
[
n
]
=
1
arq
N
n
1
r
The probability of n retransmissions is the product of failure in the n-1 transmissions and
the probability of success at the n th transmission:
p
[
n
]
=
(
PER
)(
PER
)
n
1
N
Thus, we evaluate the average number of retransmissions N in one hop:   Search WWH ::

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