Information Technology Reference
In-Depth Information
∞
=
N
=
p
[
n
]
×
n
N
n
1
The number of packets that arrive with error at the sink node can be defined for the
packets without ARQ as the product of the total number of transmitted packets
n
pac
and the
probability that the packet arrives with error at the sink node:
n
=
(
−
P
)
×
n
error
narq
pac
Considering perfect error detection of the CRC code and infinite retransmissions, none of
the ARQ packets is received with errors and thus
n
error
= 0:
n
=
(
−
P
)
×
n
=
0
error
arq
pac
The reliability
R
is given by the percentage of the sent packets being delivered correctly
to the sink node and it may be evaluated as:
R
=
[(
n
−
n
)
/
n
]
pac
error
pac
Since no specific hardware is being used, the energy consumption in the transmission and
reception of the packets is expressed only in normalized terms. While the energies spent in
coding and decoding processes were not considered in [11], [12] and [13], in [10] their effect
on energy efficiency were shown to be negligible compared to the energy consumed in the
transmission of additional parity bits. Thus, only the parity bits of the error control schemes
are considered.
The same model of [7] is considered, where the energy consumed per bit is constant and
the reception of a determined number of bits consumes approximately 75 per cent of the
energy spent to transmit the same number of bits. The minimum energy consumed
E
min
for
H
hops is evaluated for a packet without error control:
(
)
E
=
H
×
n
×
n
+
n
×
0
.
75
min
pac
aux
1
aux
1
where
n
aux1
is the total number of bits of the AUX1 packet. The total energy consumed
E
in a
sensor network for a packet without ARQ and without CRC corresponds to the total number
of bits transmitted and received, where each transmitted bit consumes 1 unit of energy and
each received bit consumes 0.75 units of energy:
(
)
E
=
H
×
n
×
n
+
n
×
0
.
75
pac
bits
bits
where
n
bits
is the total number of bits of a packet, including the access code, header and
payload.
On the oth
er
hand, for the packets with ARQ and CRC and average number of
retransmissions
N
, the energy
E
is:
