Signal Processing for High-Speed Links - Signal Processing Systems - page 326

3.1 Modulation Formats

NRZ is the dominant modulation format for both back-plane and optical links.
However, other more spectrally-efficient techniques have also been explored. In
back-plane, modulation formats such as 4-PAM [ 36 ] and more recently duobinary
(DB) [ 20 , 40 ] have been explored. Duobinary has also been explored for optical links
[ 11 ] . Duobinary modulation refers to the use of a controlled amount of ISI in the
transmitted signal or in the composite channel response. In back-plane channels,
duobinary is implemented by modulating the amplitude while in optical links, it
is implemented using phase modulation. The transmitted power spectrum of DB-
modulated signals is roughly half that of NRZ modulation resulting in reduced ISI
induced by the channel.

3.2 Adaptive Equalization

In practice, the channel in high-speed links are unknown. Therefore, adaptive
equalization techniques are needed that can learn the channel parameters via a
process of training. Many of the adaptive equalization techniques employed in
high-speed links tend to be simplified versions of those in DSL and wireless. A
key difference being that the high data-rates in high-speed links force the designer
to explore a rich mix of analog and digital equalization approaches instead on a
predominantly digital approach as in other communication links. The baseband
output r

( t ) of a high-speed link can be written in terms of the transmitted bit

sequence d [ n ] as

∞
∑

r ( t )= d [ k ] h g ( t − kT )+ w ( t ) ,

k = − ∞

where h g ( t )= g ( t ) ∗ h ( t ) is the convolution of the transmit pulse g ( t ) with the

channel impulse response h assuming that the latter is time-invariant. It is well-

known [ 31 ] that the optimal receive filter for such a linear modulation over a
linear channel is a matched filter to the transmit pulse h g (

( t )

t ) andthatasetof

sufficient statistics for the optimal detection of the sequence d (for any criteria

of optimality) can be obtained by sampling the output of this matched filter at the
symbol-synchronous intervals, t

[ n ]

nT .
An attractive means of implementing such a matched filter when the channel
response is not known precisely in advance, is the use of an adaptive fractionally-
spaced equalizer (FSE), whose output can be written

=

N
k = 0 c k r ( nT − k τ ) ,

y [ n ]= y ( nT )= (16)

where the delay-line spacing of the N taps in the equalizer, τ , is typically a fraction

of the symbol period, i.e. τ = T / M f ,where M f = 2 is typical. The coefficients