Cryptography Reference
In-Depth Information
Figure 2.24 - Eye diagrams for modulations with (2-PSK or 4-PSK) binary symbols
for different values of roll-off factor
α
(0
.
2
,
0
.
5
,
0
.
8)
.
Having determined the global spectrum
X
(
f
)
that the transmission chain
must satisfy in order to guarantee the absence of ISI, we will now establish the
frequency characteristics of the emission and reception filters.
Optimal distribution of filtering between transmission and reception
We have seen that the reception filter must be matched to the waveform placed
at its input, that is, in our case:
g
r
(
t
)=
z
(
t
0
−
t
)
(2.132)
where
z
(
t
)
results from filtering
h
(
t
)
by the transmission filter:
z
(
t
)=
h
(
t
)
⊗
g
e
(
t
)
the frequency characteristic
G
r
(
f
)
of the reception filter being equal to:
G
r
(
f
)=
Z
∗
(
f
)exp(
−
j
2
πft
0
)
(2.133)
where
represents the conjugate operator.
Of course, the global characteristic of the transmission chain must satisfy
the Nyquist criterion, which is translated by:
∗
Z
(
f
)
G
r
(
f
)=
p
(
t
0
)
CS
α
(
f
)exp(
−
j
2
πft
0
)
(2.134)
where
CS
α
(
f
)=
X
t
0
(
f
)
is the raised-cosine spectrum of roll-off factor
α
.Inthe
previous relation we considered that the channel transmits the signal placed at
its input in its entirety.
Expressing function
Z
∗
(
f
)
from the previous relation,
Z
∗
(
f
)=
p
(
t
0
)
CS
α
(
f
)
G
r
(
f
)
exp(
j
2
πft
0
)
(2.135)
then replacing
Z
∗
(
f
)
by its expression in relation (2.133), we obtain the magni-
tude spectrum of the reception filter:
=
p
(
t
0
)
CS
α
(
f
)
|
G
r
(
f
)
|
(2.136)