mohatta2015.pdf

THE IDEA 71
estimate of symbol s 2 . Unbiased means that the average value of the estimate is
the true value. It is also an example of a soft symbol estimate because it can take
on values other than +1 and —1, which are referred to as hard symbol estimates.
Now, let's look at using n, which can be modeled as
ri = — lOsi + 9s() + n\. (4.8)
To cancel interference from si on « 2 , we would multiply r\ by —0.09 and add it to
z 2 . This would give
which can be modeled as
where
z 2 = -0.1r 2 -0.09n, (4.9)
¿2 = S 2 + Ù2, (4.10)
«2 = -0.81s 0 + (-0.09ni - 0.1n 2 ). (4.11)
Compared to (4.7), we have traded the ISI term —0.9si for the term —0.81soi
reducing ISI! As long as the additional noise term is not too large, we win. We can
continue the process, using rn to cancel interference from so and so on. A block
diagram of linear equalization is given in Fig. 4.2.
W, H
'm
Q
| ► delay
/ m-1
0- + < 1
Figure 4.2
- ^ ·
1
< > -
sign(·)
LE block diagram.
Recall that we were attempting a zero-forcing strategy, forcing ISI from adjacent
symbols to be zero. In this case we ended up with a partial ZF solution, because
it forced ISI from Si to zero, but did not force ISI from s () to be zero. If we were
allowed to use ro, we could also force ISI from s