mohatta2015.pdf
signal processing from power amplifier operation control point of view
signal processing from power amplifier operation control point of view
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58 ZERO-FORCING DECISION FEEDBACK EQUALIZATION<br />
If we only use y\ to detected s\ (we ignore the copy of s\ in r-ι), then we have forced<br />
the ISI to zero.<br />
Second, to ensure that the coefficient in front of s\ is positive, we need to multiply<br />
by a number with the same sign of the channel coefficient in front of S\. Instead of<br />
— 10, let's use —1/10, giving the decision variable<br />
The detected symbol value is then<br />
2i=-0.1yi = -0.1[n-9e o ]. (3.4)<br />
si=sign{zi}. (3.5)<br />
Now we can detect S2 using ri and so on.<br />
We can understand how DFE works graphically in Fig. 3.1. There are two copies<br />
of si, one in r\ and one in r 2 . The copy in r\ has interference from so, which is<br />
removed through subtraction. The copy in ri has interference from S2, which is<br />
avoided by not using ri. We call this approach zero-forcing (ZF), because we have<br />
forced the ISI to be zero (assuming our value for So is correct). A block diagram of<br />
the ZF DFE is given in Fig. 3.2.<br />
Figure 3.1<br />
Received signal for DFE.<br />
Let's try it out on the Alice and Bob example. Recall that r\ = 1 and ri = —7.<br />
Suppose we are told that so = +1, which happens to be the correct value. The<br />
DFE output for s\ would be<br />
z 1 = -0.1 [1 - 9(+l)] = 0.8, (3.6)<br />
giving a detected value of s(l) = +1. The true value happens to be s(l) = +1, so<br />
the detected value is correct. To detect «2 we form<br />
«2 = -0.1«/2 = -0.1[-7 - 9(+l)] = 1.6, (3.7)<br />
giving s(2) = +1. This detected value is also correct, as the true value happens to<br />
be s(2) = +1. Thus, if we start with a correct value for so, we detect correct values<br />
for the remaining symbols.