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3.14 Adaptive DSP Algorithms 83

Figure 3.20b illustrates another group of related applications (prediction,
spectral estimation, and spectral whitening), while Figure 3.20c shows the setup
for equalization and deconvolution. Equalizers are required in high-speed modems
to compensate for channel distortion when data are to be transmitted over a radio
channel. This type of filter is therefore called a channel equalizer. Finally, Figure
3.20d depicts the system identification problem, which differs from the previous
cases in that the filter coefficients are of interest, whereas in the former cases the
output of the adaptive filter or error signal is the relevant result. Other applica-
tions involving adaptive DSP algorithms are echo cancellers, speech and image
coders, beamforming in sensor arrays, system modeling, and control systems [12,
17,23, 32, 36].
Both FIR and IIR filters are useful for adaptive filters, but FIR filters are
more widely used because they are much simpler. The FIR filters have only adjust-
able zeros and they are therefore always stable. However, the stability of interest
in adaptive filters is the proper adjustment of the filter coefficients. In this sense,
adaptive FIR filters are not always stable. A drawback of using only FIR filters is
that the required filter degree may become large if the channel characteristics are
unfavorable. In such cases an adaptive IIR filter may be appropriate.
An important consideration in designing adaptive filters is the criterion used
for optimizing the adjustable filter coefficients. Here we will discuss the most fre-
quently used criteria: the least mean square error and the least square error.

3.14.1 LMS (Least Mean Square) Filters
Equalization of a transmission channel
(for example, a radio channel for a
mobile phone employed for digital trans-
mission) can be achieved by placing an
equalizing filter that compensates for
nonideal channel characteristics in front
of the receiver. Figure 3.21 shows the
main block in a such a transmission sys-
tem. The problem is that the time-vari-
ant channel distorts the transmitted
pulses so that they interact and compli-
cate their detection. The role of the
adaptive filter is to compensate for the
distortion so that the intersymbol inter-
ference is eliminated.
The principle of an adaptive filter
algorithm is based on minimization of
the difference between the filter output
j
rrr,
,.
f,-..
and a reference sequence. I he filter Figure 3.21 Typical transmission system
coefficients are updated according to
some algorithm so that the error is minimized. The least mean square (LMS) error
criterion is often used because of its low computational complexity, but algorithms
with similar complexity, using the least squares (LS) criterion, have recently
become available [24, 32, 36].