mohatta2015.pdf
signal processing from power amplifier operation control point of view
signal processing from power amplifier operation control point of view
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
104 MMSE AND ML DECISION FEEDBACK EQUALIZATION<br />
which implies<br />
h = wl/wi. (5.27)<br />
Now that we have X2, we can subtract the influence of si used the detected value.<br />
However, x\ now has a copy of s^ as well. So, now we need to also subtract the<br />
influence of s\ on x\, We can then use the result to detect «2 with a weighted sum:<br />
where<br />
«2 = viwVw + W42/4, (5.28)<br />
2/3 = xi - (wic + w 2 e)si (5.29)<br />
2/4 — %2 — ( e + hc)s\. (5.30)<br />
This looks like another MMSE linear equalization design problem. Thus, we can<br />
use MMSE linear equalization design, with models for y :i and 2/4, to determine good<br />
values for w-.t, and w\ (see the Problems).<br />
5.3 THE MATH<br />
Similar to Chapter 4, MMSE and ML formulations are given. Other design criteria<br />
are not discussed, as they would be the same as in the previous chapter.<br />
Performance results are also provided.<br />
5.3.1 MMSE solution<br />
With MMSE DFE, the received signal is initially processed by a partial MF, producing<br />
received sample vectors. These sample vectors are processed by a forward<br />
filter, which collects signal energy and suppresses ISI from future symbol periods.<br />
The FBF removes ISI from past symbol periods. Unlike the chapter on ZF DFE,<br />
we allow for arbitrary pulse shaping, fractionally spaced sampling, and arbitrary<br />
path delays.<br />
The design of the MMSE FBF is similar to the design of the ZF FBF. Detected<br />
symbols are modulated and channel filtered and then subtracted from the received<br />
samples. Design of the MMSE forward filter is similar to the design of the MMSE<br />
linear equalizer. The only difference is that the FF works on modified received<br />
samples, modified to remove ISI from past symbol blocks. This simply changes<br />
the computation of the data correlation matrix R. Compared to the ZF FF, the<br />
MMSE FF works on future samples in addition to the current sample. Like matched<br />
filtering, this allows better collection of symbol energy.<br />
Assuming partial matched filtering at the front end, recall from (1.23) and (2.59)<br />
that the received samples can be modeled as<br />
where<br />
oc<br />
v{qT s ) |= y/W, Σ M« 7 '» - m7 ')s(m) + n{qT s ), (5.31)<br />
m= — 00<br />
£-1<br />
h(t) = ^gtRpit-Ti). (5.32)