mohatta2015.pdf

THE MATH 85
power is much larger than the ISI, ML, and MMSE linear equalization will behave
like matched filtering. At the other extreme, if the noise power is negligible, ML
and MMSE linear equalization will tend towards a minimum ISI solution, trying to
"undo" the channel.
The expression in (4.95) can also be used to derive a bound on DFE output
SINR, which involves assuming perfect decision feedback. We will explore this in
the next chapter.
4.3.4 Other design criteria
While the focus has been on the MMSE and ML criteria, other criteria can be used
in the design of linear equalizers. Criteria which lead to designs that do not perform
as well are the following.
Zero-forcing (ZF) We have already seen examples of full ZF and partial ZF.
Minimum ISI When full ZF is not possible, minimum ISI is better than partial
ZF.
Minimum noise This is included for completeness. It leads to matched filtering.
Minimum distortion The idea here is to minimize the worst case ISI realization.
If c m are the symbol coefficients after equalization, then the idea is to minimize
λ-,τη,τηφπι,, l c »»»l·
Note that the MMSE solution tends towards the minimum noise solution (matched
filtering) at low SNR and the minimum ISI solution at high SNR.
The following criterion lead to designs with equivalent performance to the MMSE
design.
Max SINR We showed by example how this criterion leads to a design with the
same performance as the MMSE design.
Other criteria which lead to better performance, if measured in terms of error
rate, are
Minimum symbol error rate and
Minimum bit error rate.
The design procedures are more difficult, as the discrete nature of the ISI must be
accounted for. However, the gains in performance are typically small because of
the solution being constrained to be linear.
4.3.5 Fractionally spaced linear equalization
LE is fractionally spaced when the sampling period T s is less than the symbol period
T. A common approach is to sample at twice the symbol rate (T s — 0.5Γ). Another
option is to sample at four times the symbol rate but not use all the samples for a
given symbol, giving an effective spacing of 0.75T.