mohatta2015.pdf

CHAPTER 2
MATCHED FILTERING
In this chapter, we explore matched filtering (MF). Some might argue that MF is
not really a form of equalization. However, MF provides a reference for the case
of no ISI, and it can be used as a building block in certain forms of equalization.
Also, if we assume that ISI is perfectly subtracted, MF provides a commonly used
bound on performance.
2.1 THE IDEA
Matched filtering is about collecting signal energy. Consider the dispersive scenario,
illustrated in Fig. 2.1. Suppose we are interested in detecting (determining) the
value of s\. There are two copies of si, one in r\ and one in r 2 . We would like to
combine these two copies to get a clearer picture of s\. We will call the combined
value the decision variable because we will use the combined value to decide what
symbol was sent.
Since the channel coefficients can be positive or negative, we can't simply add the
two copies together. However, if we multiply each copy by its channel coefficient,
we ensure that the sign of the channel coefficient is removed. We also give more
weight to stronger copies, which is a good strategy in dealing with the noise. Thus,
we would form the decision variable z\ given by
zi = -10n+9r 2 . (2.1)
Channel Equalization for Wireless Communications: From Concepts to Detailed 31
Mathematics, First Edition. Gregory E. Bottomley.
(c) 2011 Institute of Electrical and Electronics Engineers, Inc. Published 2011 by John Wiley & Sons, Inc.