mohatta2015.pdf

108 MMSE AND ML DECISION FEEDBACK EQUALIZATION
5.4 MORE MATH
In Chapter 3, we explored the zero-forcing (ZF) solution. Here we will focus on the
MMSE and ML formulations. We will also discuss simpler ways of modeling ISI,
which lead to simpler equalizer formulations. Discussions of block and sub-block
forms are given, and group DFE is briefly examined.
5.4.1 MMSE solution
The formulation in the more general case is similar to that for MMSE linear equalization,
except that ISI from past symbol blocks is removed. As in the previous
chapter, a chip-level formulation is used. In summary, the decision variable is
formed using
where
4 1 ," ) ( fn o) = wH y· ( 5·48 )
y = [y T (d„T s ) ... y T (dj„ 1 T s )] T (5.49)
N, K-\ , . mo-1
y{qT s ) = v(T s )-Y^J2s/E^(k) Σ \¿£ m {qT s -mT)sf{m). (5.50)
Notice we have assumed all transmitted symbols are being detected. Often we are
only interested in symbols from one transmitter. We will consider this case later.
-2 0 2 4 6 8 10 12 14
Eb/NO (dB)
Figure 5.4 BER vs. E b /N 0 for QPSK, root-raised-cosine pulse shaping (0.22 rolloff),
static, two-tap. symbol-spaced channel, with relative path strengths 0 and -1 dB. and path
angles 0 and !)() degrees, MMSE LE and DFE results.