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a multi-hop network) even if it contains errors, so wasting energy. In the BCH2 packet this
fact does not happen, but the packet has additional 16 bits for the CRC implementation.
Another modification is to use the same Hamming code of the DMx packets in the AUX1
payload, but without retransmission, with and without CRC (HAM and HAM2 packets,
respectively). Other new packet is the AUX2, which is an AUX1 packet with CRC code.
Table 2 shows the error control information for the new introduced packet types.
Table 2. Packet types with custom error control
Data
(bytes)
Packet
Time-
slots
FEC
ARQ
CRC
AUX2
1
0-27
No
No
Yes
Hamming
(15,10)
HAM
1
0-18
No
No
Hamming
(15,10)
HAM2
1
0-18
No
Yes
BCH
(232,156)
BCH
1
0-17
Yes
Yes
BCH
(232,156)
BCH2
1
0-17
No
Yes
BCH
(232,156)
BCH3
1
0-17
No
No
A NALYTICAL M ODEL
In this section it is presented an analytical model to evaluate the performance of the
Bluetooth packets. In order to investigate expressions for performance analysis, a method is
used based on [7] and [13] to evaluate the packet error probabilities. A received packet is not
accepted when any of the five events happens: (A) the destiny fails to synchronize with the
access code of the received packet; (B) the header of the received packet is corrupted (after
the repetition code is decoded); (C) the data of the received packet are corrupted after the
channel code, if any, is decoded, causing the CRC check to fail; (D) the source is unable to
synchronize with the access code of the return packet and (E) the header of the return packet
is corrupted.
The synchronization is made correlating the demodulator output with a stored copy of the
access code. A packet is synchronized if the correlator output exceeds a given threshold T .
The frame is synchronized if at least T of the 72 bits of the access code were properly
demodulated ( T = 65 in this work, the same value used in [7, 13]). The errors are assumed to
be independently distributed. The synchronization with the received packet occurs if there are
no more than (72 - T ) errors in the received access code:
72
=
T
[
] [
] ,
72
k
72
k
P
[
A
]
=
p
(
γ
)
1
p
(
γ
)
f
f
k
k
0
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