mohatta2015.pdf

MORE DETAILS 59
1/c
r m —►
H
i
,r
*\ J
z
ψ
sign^j
φ
C x y*—~ ^e'ay Α —
Figure 3.2
ZF DFE block diagram.
Now suppose we are told so = —1, the incorrect value. Then,
« 1 = -0.1[l-9(-l)] = -1.0,
(3.8)
giving a detected value of s(l) — — 1, which is incorrect. Then,
z 2 = -O.I3/2 = -0.1[-7 - 9(-l)] = -0.2,
(3.9)
giving s(2) = — 1, which is also incorrect. Thus, if we start with an incorrect value
for so, we detect incorrect values for the remaining symbols. This is called error
propagation.
3.2 MORE DETAILS
So how well does the ZF DFE work in general? It depends. If we have high
input SNR (performance is limited by ISI) and the decisions are all correct (ISI is
completely removed), then it works well. However, sometimes we make an incorrect
decision. This causes an incorrect subtraction of ISI for the next symbol, increasing
the chances of making a second incorrect decision, and so on.
How does it compare to MF? If performance is noise limited (low input SNR), we
actually do worse than MF because we don't collect all the signal energy together.
Instead, we only keep the signal energy in r\ (—lOsi) and treat the term 9si in r 2
as a nuisance to be subtracted later. Thus, at low SNR, MF will perform better.
However, at high SNR, performance is limited by ISI. If the detected values are
correct most of the time, ISI is reduced and DFE will perform better than MF.
We can determine an upper bound on output SINR by assuming correct subtraction
of ISI. In this case, y\ can be modeled as
2/1 -lOsi + n\. (3.10)