Generalized Partial Response for Equalized Channels with Rational Spectra

Harashima and Miyakawa [1] and Tomlinson [2] have described a generalized partial response technique which achieves the performance of the decision-feedback equalizer without the error propagation problem. We show here that when the equalized and baud-rate sampled channel assumes the special rational
z
transform
F(Z) =\frac{\sum\min{i=0}\max{M}{g_{i}Z^{i}}{1/L\sum\min{i=0}\max{N}{l_{i}Z^{i}
where
l_{0} = L, g_{0} = 1
, the
gi
and
li
are integers, and
L
is a power of 2, the implementation can assume an especially simple form not requiring the storage of analog samples. The numerator polynomial can be chosen to achieve transmission zeros, as in ordinary partial response, while the denominator can be chosen to reduce the noise enhancement in equalization. This technique results in as much as a doubling of the peak transmitted voltage and, as in ordinary partial response, an increase in the number of received levels. It is shown that on the
f^{1/2}
channel characteristic of coaxial cable, most of the noise advantage of decision-feedback equalization can be achieved with a moderate number of received levels, and that some of this noise advantage can be traded for a reduced number of received levels. The greatest advantage accrues in multilevel transmission because of the lower peak transmitted voltage penalty.