Precoding
The data symbols are manipulated such that
y
k
kT=
a
k
u0+ISI+νkT
y
k
k
T
a
k
u
0
ISI
ν
k
T
(1)
Design of Bandlimited Modulation Signals
Recall that modulation signals are
X
t
=∑n=-∞∞
a
n
st-nT
X
t
n
a
n
s
t
n
T
(2)
We can design
st
s
t
such that
unT=largeifn=0zero or smallifn≠0
u
n
T
large
n
0
zero or small
n
0
(3)
where
ykT=
a
k
u0+∑n=-∞∞
a
n
ukT-nT+νkT
y
k
T
a
k
u
0
n
a
n
u
k
T
n
T
ν
k
T
(ISI is the sum term, and once again,
n≠k
n
k
.)
Also,
ynT=s¯g¯
h
opt
nT
y
n
T
s
g
h
opt
n
T
The signal
st
s
t
can be designed to have reduced ISI.
Design Equalizers at the Receiver
Linear equalizers or decision feedback equalizers reduce ISI
in the statistic
y
t
y
t
Maximum Likelihood Sequence Detection
ykT=∑n=-∞∞
a
n
kT-nT+νkT
y
k
T
n
a
n
k
T
n
T
ν
k
T
(4)
By observing
yT
,
y2T
,
…
y
T
,
y
2
T
,…
the date symbols are observed frequently. Therefore, ISI can
be viewed as diversity to increase performance.