mohatta2015.pdf

104 MMSE AND ML DECISION FEEDBACK EQUALIZATION
which implies
h = wl/wi. (5.27)
Now that we have X2, we can subtract the influence of si used the detected value.
However, x\ now has a copy of s^ as well. So, now we need to also subtract the
influence of s\ on x\, We can then use the result to detect «2 with a weighted sum:
where
«2 = viwVw + W42/4, (5.28)
2/3 = xi - (wic + w 2 e)si (5.29)
2/4 — %2 — ( e + hc)s\. (5.30)
This looks like another MMSE linear equalization design problem. Thus, we can
use MMSE linear equalization design, with models for y :i and 2/4, to determine good
values for w-.t, and w\ (see the Problems).
5.3 THE MATH
Similar to Chapter 4, MMSE and ML formulations are given. Other design criteria
are not discussed, as they would be the same as in the previous chapter.
Performance results are also provided.
5.3.1 MMSE solution
With MMSE DFE, the received signal is initially processed by a partial MF, producing
received sample vectors. These sample vectors are processed by a forward
filter, which collects signal energy and suppresses ISI from future symbol periods.
The FBF removes ISI from past symbol periods. Unlike the chapter on ZF DFE,
we allow for arbitrary pulse shaping, fractionally spaced sampling, and arbitrary
path delays.
The design of the MMSE FBF is similar to the design of the ZF FBF. Detected
symbols are modulated and channel filtered and then subtracted from the received
samples. Design of the MMSE forward filter is similar to the design of the MMSE
linear equalizer. The only difference is that the FF works on modified received
samples, modified to remove ISI from past symbol blocks. This simply changes
the computation of the data correlation matrix R. Compared to the ZF FF, the
MMSE FF works on future samples in addition to the current sample. Like matched
filtering, this allows better collection of symbol energy.
Assuming partial matched filtering at the front end, recall from (1.23) and (2.59)
that the received samples can be modeled as
where
oc
v{qT s ) |= y/W, Σ M« 7 '» - m7 ')s(m) + n{qT s ), (5.31)
m= — 00
£-1
h(t) = ^gtRpit-Ti). (5.32)