of 2(1
r
) that only the preceding or the following slot is vulnerable and a
probability of (2
r
1) that both preceding and following slots are vulner-
able. Hence the probability of the desired piconet not being disturbed by
one advisory piconet is given as:
P
s
UR
2(1
r
)
78
79
(2
r
1)
78
79
2
(21.1)
The PER due to
N
neighboring Bluetooth piconets for synchronous and
asynchronous modes are given as:
(PER)
syn
1
78
79
N
(21.2)
(PER)
asyn
1
2(1
r
)
78
79
(2
r
1)
78
79
2
N
1
(
P
s
UR
)
N
(21.3)
21.12.2 PER
from
M
Neighboring IEEE 802.11 WLANs*
Under IEEE 802.11 FH, the probability of
M
IEEE 802.11 induced collisions on
a Bluetooth packet is given as [17]:
PER
1
1
G
L
78
79
\
H/L
]
G
L
78
79
\
H/L
]
G
/
G
M
(21.4)
Under IEEE 802.11 DS, the probability of
M
IEEE 802.11 induced collisions
on a Bluetooth packet is given as:
PER
1
1
G
L
57
79
\
H/L
]
G
L
57
79
\
H/L
]
G
/
G
M
(21.5)
where:
H
the duration of a Bluetooth packet
L
the dwell period of an IEEE 802.11 transmission
T
w
the packet duration of IEEE 802.11
G
L
H
/
L
M
L
T
w
H
L
x
M
the least integer greater than or equal to
x
The collision probability of a Bluetooth piconet where there are
N
neighboring
Bluetooth piconets and
M
IEEE 802.11 WLANs will be:
(PER)
syn
1
78
79
N
(
P
s
)
M
(21.6)
* Refer to Reference [17] for the derivation of equations and details.
