mohatta2015.pdf

58 ZERO-FORCING DECISION FEEDBACK EQUALIZATION
If we only use y\ to detected s\ (we ignore the copy of s\ in r-ι), then we have forced
the ISI to zero.
Second, to ensure that the coefficient in front of s\ is positive, we need to multiply
by a number with the same sign of the channel coefficient in front of S\. Instead of
— 10, let's use —1/10, giving the decision variable
The detected symbol value is then
2i=-0.1yi = -0.1[n-9e o ]. (3.4)
si=sign{zi}. (3.5)
Now we can detect S2 using ri and so on.
We can understand how DFE works graphically in Fig. 3.1. There are two copies
of si, one in r\ and one in r 2 . The copy in r\ has interference from so, which is
removed through subtraction. The copy in ri has interference from S2, which is
avoided by not using ri. We call this approach zero-forcing (ZF), because we have
forced the ISI to be zero (assuming our value for So is correct). A block diagram of
the ZF DFE is given in Fig. 3.2.
Figure 3.1
Received signal for DFE.
Let's try it out on the Alice and Bob example. Recall that r\ = 1 and ri = —7.
Suppose we are told that so = +1, which happens to be the correct value. The
DFE output for s\ would be
z 1 = -0.1 [1 - 9(+l)] = 0.8, (3.6)
giving a detected value of s(l) = +1. The true value happens to be s(l) = +1, so
the detected value is correct. To detect «2 we form
«2 = -0.1«/2 = -0.1[-7 - 9(+l)] = 1.6, (3.7)
giving s(2) = +1. This detected value is also correct, as the true value happens to
be s(2) = +1. Thus, if we start with a correct value for so, we detect correct values
for the remaining symbols.