Information Technology Reference
In-Depth Information
Two constants a and b can be defined:
(
)
(
)
γ
γ
2
2
a
=
1
1
ρ
,
b
=
1
+
1
ρ
2
2
where γ is the instantaneous signal-to-noise ratio (SNR). The error symbol probability
p
)
for the GFSK modulation must be applied and is given by :
1
2
2
(
a +
b
)
/
2
p
(
γ
)
=
Q
(
a
,
b
)
e
I
(
ab
)
1
o
2
where Q 1 (a,b) is the Q-Marcum function and I o is the modified Bessel function of first kind.
Thus, the packet error probability of the forward channel, PER f , and reverse, PER r , can be
defined as:
PER
=
1
f
(
γ
)
P[
A]
P[
B]
P[
C]
d
γ
f
f
f
0
PER
=
1
f
(
γ
)
P[
D]
P[
E]
d
γ
r
r
r
0
where f( γ f ) and f( γ r ) are the probability density functions and γ f and γ r are SNR of the forward
and reverse channels, respectively.
The packet retransmission probability then given by
P
(
γ
,
γ
)
=
1
f
(
γ
)
P
[
A
]
P
[
B
]
P
[
C
]
d
γ
f
(
γ
)
P
[
D
]
P
[
E
]
d
γ
r
f
r
f
f
r
r
0
0
The data rate R is given by
K
R
=
,
-
6
D
N
625
10
where D is the number of occupied slots per transmission including the reverse packet, N is a
random variable representing the total number of times a particular packet must be
transmitted and K is the number of data bits in the packet (DM1:136, DM3: 968, DM5: 1792,
DH1: 216, DH3: 1464, DH5:2712, 2-DH1: 432, 2-DH3: 2936, 2-DH5: 5432, 3-DH1: 664, 3-
DH3: 4416, 3-DH5: 8168). The average throughput is the expected value of R with respect to
N ,
=
{} [
] [
]
N
1
R
=
E
R
=
1
P
(
γ
,
γ
)
P
(
γ
,
γ
)
R
r
f
r
r
f
r
N
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