mohatta2015.pdf

CHAPTER 4
LINEAR EQUALIZATION
With linear equalization, we detect a symbol by forming a weighted combination
of received values. How does it work? Nearby received values contain copies of
interfering symbols, which can be used to cancel or reduce ISI.
4.1 THE IDEA
We found that matched filtering collects signal energy, but also interference from
adjacent symbols. This is illustrated in Fig. 4.1, where the circles indicate desired
symbol terms (for S2) and the octagon-like shapes indicate interference from adjacent
symbols. We would like to subtract the contributions from these adjacent
symbols, but we don't know their values. However, we have copies of these symbols
present in other received values. As shown by squares in Fig. 4.1, there is a copy of
the previous symbol Si in τ-χ and a copy of the next symbol S3 in Γ4. By multiplying
these received values by certain numbers (called weights) and adding them to the
matched filter value, we can cancel interference from adjacent symbols.
Problem solved? Not quite. In canceling ISI from si using r\, we introduce ISI
from so as well as noise m. Similarly, canceling ISI from S3 using r^ introduces
ISI from S4 and noise n^. So now what? Well, we can use τ υ to cancel the ISI
from So and r$ to cancel the ISI from S4. This introduces more ISI terms, requiring
us to continue to introduce more received values. Are we fighting a losing battle?
Channel Equalization for Wireless Communications: From Concepts to Detailed 69
Mathematics, First Edition. Gregory E. Bottomley.
© 2011 Institute of Electrical and Electronics Engineers, Inc. Published 2011 by John Wiley & Sons, Inc.