Digital Signal Processing Reference
In-Depth Information
The other context in which the SIMO channel model arises is related to
5.2.1 Oversampling and the SIMO Model
In the previous chapters, whenever we have expressed the received signal
as the convolution of a symbol sequence and the channel impulse response
h
, we have assumed that the received signal was sampled at the symbol
rate, which is the case in several communication systems. However, if the
sampling rate is made higher than the symbol rate, the received signal can
also be represented in terms of the outputs of a SIMO channel model.
To explain this connection, let us first consider the received baseband
signal, expressed by
(
n
)
∞
x
(
t
)
=
s
(
i
)
h
(
t
−
iT
)
+
ν
(
t
)
,
(5.12)
i
=−∞
where
h
(
t
)
stands for the channel impulse response
ν
(
t
)
is the additive noise
In the usual case, when the signal is sampled at the symbol rate
T
,the
received sequence will be given by
∞
x
(
nT
)
=
s
(
i
)
h
((
n
−
i
)
T
)
+
ν
(
nT
)
.
(5.13)
i
=−∞
If we sample the received signal at a rate
P
times higher than the symbol
rate, i.e.,
1
T
s
=
P
1
T
(5.14)
then the
oversampled
sequence
x
(
nT
s
)
will be given by
x
n
T
P
h
n
T
iT
ν
n
T
P
.
∞
x
(
nT
s
)
=
=
s
(
i
)
P
−
+
(5.15)
i
=−∞
The relationship between the oversampled sequence and the SIMO
channel model is revealed when we consider sequences composed of sam-
ples of
x
(
t
)
spaced by one symbol period. For example, the samples
x
(
0
)
,
x
(
T
)
,
x
(
2
T
)
,
...
represent the sequence
{
x
(
nT
)
}
, while
x
(
T
s
)
,
x
(
T
s
+
T
)
,
