Digital Signal Processing Reference
In-Depth Information
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(a) Channel
(b) Equalizer
(c) Effective channel
FIgure 9.1
Even when a multipath channel is sparse, the corresponding linear equalizer need
not be sparse. (a) Magnitudes of channel coefficients. (b) Magnitudes of zero-forcing equalizer
coefficients. (c) Magnitudes of coefficients of resulting effective channel.
somewhat sparse, and (c) the resulting effective channel. This means there are several
ways to exploit sparsity in adaptive equalization:
•
Form an adaptive equalizer that is only somewhat sparse, as in Figure 9.1(b).
•
Form an adaptive channel identifier that exploits sparsity, then periodically
use the current estimate to compute the equalizer.
Use an alternate equalizer structure that exploits sparsity, such as a partial
•
feedback equalizer (PFE) [36], as shown in
Figure 9.2
, and adapt it via an algo-
rithm that exploits sparsity.
We now discuss these adaptive algorithms for sparse linear filters (identifiers or
equalizers).
An algorithmic paradigm that has received much attention recently due to its fast
convergence for sparse adaptive filters is the use of proportionate adaptation [37], as
proposed by Duttweiler [18]. The idea is to update large taps more quickly than small
taps, since they are more important. The many small taps do little to reduce MSE, and if
the filter is known
a priori
to be sparse, many of the small taps may actually be zero, and
their updates are noise driven. Although recent advances in proportionate adaptation
have been motivated by echo cancellation, the algorithms are equally applicable to wire-
less systems in which the channels or equalizers are known to be sparse, for example,
digital television channels. As shown in [38], a histogram of measured channel coef-
ficients for digital television (U.S. standard) follows an inverse power law distribution,
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