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.
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