EQUALIZATION - Advanced Signal Integrity for High-Speed Digital Design - page 533

n = 0

n = 1

n = 2

0.2

error

n 3

=

0.16

0.12

c2

0.08

0.04

0

c1

Figure 12-36 Adaptive equalization error “contour” and coefficient convergence.

where c k (n) is the value of the k th coefficient at time t = nT , y(n) the equalized
signal, y(n) the training signal, and k a scaling factor that controls the rate of

coefficient adjustment. The adaptive ZFS approach has the advantage that it is
very easy to implement but has the drawback that it does not comprehend ISI
that occurs outside the length of the equalizer.
Another class of adaptive algorithms is the least mean square (LMS) set of
algorithms. They attempt to minimize the mean square error of the equalizer
output at all times and are commonly used in adaptive equalizers because they
typically achieve better performance than ZFS algorithms and are relatively easy
to implement. An example is the sign-sign least mean square approach [Kim
et al., 2005]. Sign-sign LMS updates the equalizer coefficients based on the
sign of the error of the equalized signal and the sign of the input signal, as
described by

c k (n + 1 ) = c k (n) + µ sign[ y(n) − y(n) ] sign[ x(n − kT ) ] (12-30)

where y(n) is the estimated signal (the output from the equalizer), y(n) the

reference signal, x(n − kT ) the input to the equalizer, and µ the scaling factor.

Example 12-6 Adaptive Equalizer Operation We now compare the behavior of
the adaptive ZFS and sign-sign LMS algorithms for a two-tap equalizer (cursor
plus postcursor) as they apply to the same differential PCB channel that we