Digital Signal Processing Reference
In-Depth Information
MIMO channel
h
11
(
n
)
x
1
(
n
)
Σ
s
1
(
n
)
h
12
(
n
)
h
21
(
n
)
x
2
(
n
)
Σ
s
2
(
n
)
h
22
(
n
)
FIGURE 5.1
MIMO scenario with two transmitters and two receivers.
where the matrices
H
(
n
)
are composed of the coefficients
h
ij
(
n
)
of all
subchannels.
In fact, Equation 5.2 is very similar to that which describes the output of
a SISO system, given in (2.21). The output of a MIMO system can thus be
interpreted as the convolution between a sequence of matrices
H
(
n
)
repre-
senting the channel and the vector
s
(
n
)
composed of the sources. Hence, we
may write
x
(
n
)
=
H
(
n
)
∗
s
(
n
)
+
ν
(
n
)
(5.3)
We can also define the
z
-transform of the channel impulse response as
z
−
k
H
(
z
)
H
(
k
)
(5.4)
k
which represents a polynomial matrix, since each of its elements is a
An important classification of the MIMO systems is concerned with the
nature of combination of the input (source) signals, which leads to the
following cases:
•
Instantaneous
: In this case, the resulting signals at the receiver, apart
from the noise, are a combination of the input signals at a given time
instant, i.e., the received signal at a time instant
n
only depends on a
