mohatta2015.pdf

60 ZERO-FORCING DECISION FEEDBACK EQUALIZATION
The decision variable for si is then given by Z\ = —0.1j/i, which can be modeled as
2i=si+0.1ni. (3.11)
Assuming a noise power of 100, the resulting output SINR is 1.0, which is greater
than the MF output SINR of 0.955. Thus, in this case, we expect the ZF DFE to
perform better at high SNR (when decisions are mostly correct).
We can also determine a lower bound on output SINR by assuming incorrect
subtraction of ISI. When we subtract the incorrect value, we essentially double the
value (e.g., +1 — (—1) = 2). The model for y\ becomes
2/1 = -10s 1 +9(2s„) + ni. (3.12)
The decision variable for si is then given by z\ = — O.lyi, which can be modeled as
zi = s-i +1.8s()+0.1m. (3.13)
The resulting output SINR is 0.236, which is much lower.
Is zero-forcing the best strategy? While it eliminates ISI, it doesn't account for
the loss of signal energy by ignoring the second copy of the symbol of interest in r 2 .
It turns out that we can use future samples to recover some of this loss. However,
then we can't entirely eliminate ISI. This will be explored in Chapter 5.
In the general dispersive scenario, for s m , we form the decision variable
and detect Sfc using
The upper bound on output SINR is then
ym=r m -dê m -i (3.14)
s m = sign{cy m }. (3.15)
SINR