mohatta2015.pdf

CHAPTER 5
MMSE AND ML DECISION FEEDBACK
EQUALIZATION
Decision feedback equalization (DFE) uses past symbol decisions (detected values)
to remove ISI from previous symbols. MMSE and ML DFE perform a trade-off
between collecting signal energy and introducing ISI from future symbols.
5.1 THE IDEA
Consider detection of symbol si. Recall that there are two copies of si, one is r\
and one in r 2 . Specifically,
r\ = — 10si+9so + ni
r 2 = -10s 2 +9si + n 2 . (5.1)
In Chapter 3, we used ri to detect «i, subtracting ISI from sn first. We avoided
ISI from future symbols by ignoring the copy of si in r 2 . We would like to take
advantage of the copy of Si in r 2 . In Chapter 4, with linear equalization, we
examined the MMSE strategy. We can use that strategy here as well.
As in Chapter 3, we first remove the influence of so on r\, giving
which, assuming s 0 = s 0 , can be modeled as
2/1 = 7·!- 9s 0 , (5.2)
3/1 =-lOsi+ni. (5.3)
Channel Equalization for Wireless Communications: From Concepts to Detailed 99
Mathematics, First Edition. Gregory E. Bottomley.
© 2011 Institute of Electrical and Electronics Engineers, Inc. Published 2011 by John Wiley & Sons, Inc.