mohatta2015.pdf

102 MMSE AND ML DECISION FEEDBACK EQUALIZATION
Figure 5.2
MMSE DFE block diagram.
Let's revisit the Alice and Bob example. Recall that r\ = 1 and r 2 = —7.
Suppose we are told that so = +1, the correct value. The MMSE DFE output for
s i would be
2, = (-0.04158)(1 - 9(+l)) + (0.01871)(-7) = 0.202, (5.14)
giving a detected value of s(l) = +1, the correct value. To detect s 2 using only r\
and r 2 , we form
z 2 = (0)(1) + (-0.05X-7 - 9(+l)) = 0.35, (5.15)
giving s(2) = +1, the correct value. Thus, if we start with a correct value for á"o,
we get the correct values for the remaining symbols.
Now suppose we are told Jo = —1, the incorrect value. We will find (see the
Problems) that we get s\ = — 1 and s 2 = +1. Thus, we can still have an error
propagation problem. However, it is not as bad, as this time we detect s 2 correctly.
In general, we expect the MMSE approach to perform better than the ZF approach.
As with the ZF DFE, we can compute an upper bound on SINR, assuming past
decisions are correct. Substituting model expressions into (5.7) gives
Z\ = M>2(-10)S2 + (lt>l( —10) + W 2 9)si + WI9(SQ — S()) + W\U\ + W2U2. (5.16)
The second term is the signal term and has average power
S = (-10w l +9w 2 ) 2 . (5.17)
The third term is zero due to our assumption of correct past decisions. The remaining
terms are impairment and have power
I + N = w|l00 + (wf + »1)100. (5.18)