Digital Signal Processing Reference
In-Depth Information
Optimal transceivers for
diagonal channels
11.1 Introduction
Consider a transceiver system of the form shown in Fig. 11.1. For a fixed channel
H
and noise statistics, an important problem is the optimization of the precoder
F
and equalizer
G
in order to minimize an appopriate objective function such
as the mean square reconstruction error or the bit error rate. In this chapter
we consider this problem for the simple special case where the channel transfer
matrix
H
is an
M
×
M
diagonal matrix
⎡
⎣
⎤
⎦
H
0
0
...
0
0
H
1
...
0
H
=
.
.
.
(11
.
1)
.
.
.
00
...
H
M−
1
with independent additive Gaussian noise sources
q
k
(
n
) as shown in Fig. 11.2.
We can regard this as a single-user system, where
s
k
(
n
) is obtained from a
signal
s
(
n
) by blocking or parsing (see Secs. 3.5 and 3.6);
s
k
(
n
) could be the
k
th
frequency bin in the DMT or OFDM system, for example. We can also regard
this as an
M
-user communication system, provided it is practicable to collect
the
M
signals in one transmitting location for common processing.
370
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