Signal Processing for High-Speed Links - Signal Processing Systems - page 328

FFE structures are typically implemented with analog tapped delay-line circuits in
CMOS, where the cost (and therefore the power consumption) of a transceiver need
to be kept to a minimum. Challenges include the realization of accurate, low-loss
delay-lines, such that the spacing

between adjacent taps are equal and equal to a
fraction of the bit-period, and that the signal does not decay too substantially as it
is passed from the input to the end of the delay line. For symbol decisions d

τ

[ n ]= 1

d d

for y [ n ] > η and [ n ]= 0for y [ n ] ≤ η and error signal e [ n ]=( [ n ] − y [ n ]) ,the

coefficient update algorithms using LMS, for step-size μ ,

c k [ n ]= c k [ n − 1 ]+ μ r ( nT − k τ ) e [ n ] , k = 0 , 1 ,..., N − 1

need not be overly complex, since the resolution with which the multiplications ( 16 )
can be carried out is limited.
FFEs are not particularly well-suited to channels with deep spectral nulls such
as those in back-plane channels with discontinuities. For such channels, the DFE
showninFig. 9 , is a natural extension of the FFE. A DFE typically consists of
an FFE with an additional linear (or non-linear) filter used to process past symbol
decisions

d

in order to cancel post-cursor ISI. Assuming past symbol decisions
are correct, then the FFE portion of a DFE converts as much of the pre-cursor ISI
as possible, within its degrees of freedom, into post-cursor ISI, the effects of which
will be subtracted off by the feedback filter. The output of the DFE with a linear
feedback filter is given by

[ n ]

N 1 − 1

k = 0

N 2
j = 1 b j [ n ] d [ n − j ] ,

y [ n ]= c k [ n ] r ( nT − k τ ) − (17)

whose LMS coefficient updates are given by

c k [ n ]= c k [ n − 1 ]+ μ r ( nT − k τ ) e [ n ] , k = 0 , 2 ,..., N 1 − 1 (18)

d

b j [ n ]= b j [ n − 1 ]+ μ [ n − j ] e [ n ] , j = 1 , 2 ,..., N 2 . (19)

3.3 Equalization of Nonlinear Channels

Unlike back-plane and MMF channels, the SMF channel is non-linear. This is due
to the presence of a direct (square-law) O/E detector in the receiver front-end.
As a result, there is no discrete-time equivalent baseband channel, and adaptive
equalization techniques, such as the FFE or DFE discussed previously, do not
provide much benefit for SMF applications. Some success for small amounts of
CD has been achieved using sub-optimal techniques such as DFEs with state-
dependent thresholds [ 39 ] or with nonlinear feedback taps, i.e. where the feedback
filter contains not only prior detected bits, but also pairwise products [ 41 ] .