Cryptography Reference
In-Depth Information
mined using a computer. Figure 3.3 gives the result of the calculation for some
PSK and QAM modulations.
Figure 3.3 - Capacity of some modulations.
Capacity of the Rayleigh channel
Let there be a Rayleigh channel whose attenuation is denoted
α
.Fordiscrete
equiprobable inputs (a case similar to the Gaussian channel treated above),
(3.14) is always applicable. There are two cases, conditioned by the knowledge
of the attenuation
α
of the channel, or not.
In the case where
α
is not known
a priori
, we write the conditional probability
density of the Rayleigh channel in the form:
+
∞
p
(
y
|
x
i
)=
p
(
α
)
p
(
y
|
x
i
,α
)
d
α
−∞
α
2
exp
d
α
+
0
∞
2
α
exp
−
−
|
y
−α
x
i
|
2
2
σ
2
1
√
2
πσ
2
=
One development of this expression means that we can explicitly write this
conditional probability density that turns out to be independent of
α
:
+2
x
i
y
e
−
|
y
|
2
x
i
)=
σe
−
|
y
|
2
|
x
i
|
2
+2
σ
2
(
|
x
i
|
2
+2
σ
2
)
3
/
2
2
π
2
σ
2
|
x
i
|
2
+2
σ
2
p
(
y
|
1
2
erfc
x
i
y
σ
2
(
|
x
i
|
2
+2
σ
2
)
1
×
−
