Cryptography Reference
In-Depth Information
Figure 2.22 - Eye diagram of an (a) ISI and (b) ISI-free 2-PSK modulation.
positioning errors of the sampling time. In the presence of ISI, the different
plots of
p
(
t
)
no longer pass through a single point at the sampling time and the
ISI contributes to closing the eye diagram.
The output of the reception filter at time
t
0
+
nT
of the in-phase component
of the receiver is equal to:
y
c
(
t
0
+
nT
)=
Aa
n
p
(
t
0
)+
A
i
=0
a
n−i
p
(
t
0
+
iT
)
A
i
(2.114)
−
b
n−i
q
(
t
0
+
iT
)
−
√
M
)
p
(
t
0
)
,for
j
=
For a M-QAM modulation, the useful signal is
A
(2
j
−
1
,
√
M
and the decision is taken by comparing signal
y
c
(
t
0
+
nT
)
to a set
of thresholds separated by
2
p
(
t
0
)
. There will be errors in the absence of noise if
the ISI, for certain configurations of symbols
c
i
, is such that the received signal
is situated outside the correct decision zone. This occurs if the ISI is higher in
absolute value to
p
(
t
0
)
. This situation is translated by the following condition:
1
,
···
Max
a
n−i
,b
n−i
a
n−i
p
(
t
0
+
iT
)
−
b
n−i
q
(
t
0
+
iT
)
>
|
p
(
t
0
)
|
i
=0
i
Taking into account the fact that the largest value taken by symbols
a
i
and
b
i
is
√
M
−
1
, the previous condition becomes:
i
=0
|
+
i
|
p
(
t
0
+
iT
)
|
q
(
t
0
+
iT
)
|
D
max
=(
√
M
−
1)
≥
1
(2.115)
|
p
(
t
0
)
|
Quantity
D
max
is called the maximum distortion. When the maximum distor-
tion is greater than unity, the eye diagram is closed at the sampling time and
errors are possible, even in the absence of noise.