Digital Signal Processing Reference
In-Depth Information
where H is defined as
⎡
⎤
h
(
0
)
h
(
1
)
···
h
(
N
−
1
)
0
···
0
⎣
⎦
0h
(
0
)
···
h
(
N
−
2
)
h
(
N
−
1
)
0
H
=
. (5.44)
.
.
.
.
.
.
.
.
.
.
.
.
0
0
···
h
(
0
)
h
(
1
)
···
h
(
N
−
1
)
5.2.4 Fractionally Spaced Equalizers and the MISO Equalizer Model
Let us assume the equalizer to be an FIR filter, composed of
KP
coefficients, i.e.,
=
w
T
s
)
T
.
w
(
0
)
w
(
T
s
)
w
(
2
T
s
)...
w
(
T
)...
w
((
KP
−
1
)
(5.45)
The difference in this case is that two adjacent elements are related to sam-
ples delayed by a fraction of the symbol interval, the reason why this is called
an
FS equalizer
. Its output is given by
KP
−
1
w
lT
s
x
nT
s
lT
s
.
y
(
nT
s
)
=
−
(5.46)
l
=
0
It should be noted that the output is also oversampled, i.e., its samples are
spaced by a fraction of the symbol period. Therefore, to obtain a sequence of
T
-spaced recovered symbols one should decimate the sequence by the same
oversampling factor
P
. This decimation factor originates
P
different baud-
spaced sequences
y
nT
,
i
iT
P
y
i
(
nT
)
=
+
=
0,
...
,
P
−
1
(5.47)
and each one, in accordance with (5.46), can be expressed as
w
lT
P
x
nT
.
LP
−
1
iT
P
−
lT
P
y
i
(
nT
)
=
+
(5.48)
l
=
0
Notice that the coefficients
w
lT
s
can also be arranged into
P
baud-
spaced sequences, each one related to a subequalizer, i.e.,
w
lT
P
T
l
=
0,
...
,
K
−
1
w
k
lT
=
w
lP
k
T
s
k
+
=
+
(5.49)
k
=
...
,
P
−
0,
1
