mohatta2015.pdf
signal processing from power amplifier operation control point of view
signal processing from power amplifier operation control point of view
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CHAPTER 4<br />
LINEAR EQUALIZATION<br />
With linear equalization, we detect a symbol by forming a weighted combination<br />
of received values. How does it work? Nearby received values contain copies of<br />
interfering symbols, which can be used to cancel or reduce ISI.<br />
4.1 THE IDEA<br />
We found that matched filtering collects signal energy, but also interference from<br />
adjacent symbols. This is illustrated in Fig. 4.1, where the circles indicate desired<br />
symbol terms (for S2) and the octagon-like shapes indicate interference from adjacent<br />
symbols. We would like to subtract the contributions from these adjacent<br />
symbols, but we don't know their values. However, we have copies of these symbols<br />
present in other received values. As shown by squares in Fig. 4.1, there is a copy of<br />
the previous symbol Si in τ-χ and a copy of the next symbol S3 in Γ4. By multiplying<br />
these received values by certain numbers (called weights) and adding them to the<br />
matched filter value, we can cancel interference from adjacent symbols.<br />
Problem solved? Not quite. In canceling ISI from si using r\, we introduce ISI<br />
from so as well as noise m. Similarly, canceling ISI from S3 using r^ introduces<br />
ISI from S4 and noise n^. So now what? Well, we can use τ υ to cancel the ISI<br />
from So and r$ to cancel the ISI from S4. This introduces more ISI terms, requiring<br />
us to continue to introduce more received values. Are we fighting a losing battle?<br />
Channel Equalization for Wireless Communications: From Concepts to Detailed 69<br />
Mathematics, First Edition. Gregory E. Bottomley.<br />
© 2011 Institute of Electrical and Electronics Engineers, Inc. Published 2011 by John Wiley & Sons, Inc.