Digital Signal Processing Reference
In-Depth Information
q
(
n
)
s
(
n
)
s
(
n
)
M
P
J
y
(
n
)
M
x
(
n
)
F
(
z
)
H
(
z
)
G
(
z
)
equalizer
precoder
channel
Figure 1.7
. A digital communication system.
The precoder
F
(
z
) transforms this sequence
s
(
n
) into another sequence
x
(
n
).
We will see that the choice of
F
(
z
) plays an important role in the performance
of the communication system. The channel produces the inevitable distortion
represented by the transfer function
H
(
z
) and the noise vector
q
(
n
)
.
Thus the
signal obtained at the receiver is
L
y
(
n
)=
h
(
k
)
x
(
n
−
k
)+
q
(
n
)
.
(1
.
17)
k
=0
The equalizer
G
(
z
) seeks to reconstruct
s
(
n
) from this distorted version:
s
(
n
)=
k
g
(
k
)
y
(
n
−
k
)
.
(1
.
18)
The joint design of the transceiver
is an important problem in
modern digital communications. The MIMO transceiver shown in the figure can
be used to transmit messages
{
F
(
z
)
,
G
(
z
)
}
s
k
(
n
)
,
0
≤
k
≤
M
−
1
,
(1
.
19)
from
M
separate users. It can also be used to transmit information from one
user by representing the message
s
(
n
) from the user in the form of a vector
s
(
n
);
such systems are called block-based transceivers for SISO channels. They have
many advantages as we shall see. MIMO channels also arise from the use of
multiple antennas for single users; a detailed discussion of how MIMO channels
arise will be given in Sec. 4.5.
A special case of the MIMO system arises when the channel is
memoryless
,
that is, the transfer function
H
(
z
) is just a constant
H
.
This corresponds to the
situation where
L
= 0 in Eq. (1.15). Optimization of transceivers for memoryless
MIMO channels will be the focus of some of the chapters in this topic.
1.5 Scope and outline
The reader is assumed to have some familiarity with introductory topics in com-
munications and signal processing.
References for such background material
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